Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Find $straight A to the power of negative 1 end exponent$ if $straight A space equals space open square brackets table row 0 cell space space space space 1 end cell cell space space space space 1 end cell row 1 cell space space space space 0 end cell cell space space space 1 end cell row 1 cell space space space space 1 end cell cell space space space 0 end cell end table close square brackets$ Also show that $straight A to the power of negative 1 end exponent space space equals fraction numerator straight A squared minus 3 straight I over denominator 2 end fraction.$

77 Views

202.
If $straight A space equals space open square brackets table row 1 cell space space 3 end cell cell space space space 3 end cell row 1 cell space space 4 end cell cell space space 3 end cell row 1 cell space 3 end cell cell space space space 4 end cell end table close square brackets comma$ then verify that A adj A = | A | I. Also find A .

straight A space equals space open square brackets table row 1 cell space 3 end cell cell space space 3 end cell row 1 cell space 4 end cell cell space 3 end cell row 1 cell space 3 end cell cell space 4 end cell end table close square brackets

open vertical bar straight A close vertical bar space equals space open vertical bar table row 1 cell space 3 end cell cell space 3 end cell row 1 cell space 4 end cell cell space 3 end cell row 1 cell space 3 end cell cell space 4 end cell end table close vertical bar space equals space open vertical bar table row 4 cell space space 3 end cell row 3 cell space space 4 end cell end table close vertical bar minus 3 space open vertical bar table row 1 cell space 3 end cell row 1 cell space 4 end cell end table close vertical bar space plus space 3 space open vertical bar table row 1 cell space space 4 end cell row 1 cell space space 3 end cell end table close vertical bar space space space space space space space equals space 1 left parenthesis 16 minus 9 right parenthesis space minus 3 space left parenthesis 4 minus 3 right parenthesis space plus space 3 left parenthesis 3 minus 4 right parenthesis space equals space 7 minus 3 minus 3 space equals space 1 not equal to 0 therefore space space space straight A to the power of negative 1 end exponent space exists. space space space space space space straight A subscript 11 space equals space open vertical bar table row 4 cell space space 3 end cell row 3 cell space space 4 end cell end table close vertical bar space equals space 16 minus 9 space equals space 7 comma space space space space space straight A subscript 12 space equals space minus open vertical bar table row 1 cell space space space 3 end cell row 1 cell space space 4 end cell end table close vertical bar space equals space minus left parenthesis 4 minus 3 right parenthesis space equals space minus 1 space space space space space space straight A subscript 13 space equals space open vertical bar table row 1 cell space space space 4 end cell row 1 cell space space space 3 end cell end table close vertical bar space equals space 3 minus 4 space equals space minus 1 comma space space space straight A subscript 21 space equals space minus open vertical bar table row 3 cell space space space 3 end cell row 3 cell space space space 4 end cell end table close vertical bar space equals space minus left parenthesis 12 minus 9 right parenthesis space equals space minus 3 space space space space space space straight A subscript 22 space equals space open vertical bar table row 1 cell space space 3 end cell row 1 cell space space 4 end cell end table close vertical bar space equals space 4 minus 3 space equals space 1 comma space space space space straight A subscript 23 space equals space minus open vertical bar table row 1 cell space space space 3 end cell row 1 cell space space space 3 end cell end table close vertical bar space equals space minus left parenthesis 3 minus 3 right parenthesis space equals space 0 space space space space space space straight A subscript 31 space equals space open vertical bar table row 3 cell space space space 3 end cell row 4 cell space space space 3 end cell end table close vertical bar space equals space 9 minus 12 space equals space minus 3 comma space space space straight A subscript 32 space equals space minus open vertical bar table row 1 cell space space space 3 end cell row 1 cell space space space 3 end cell end table close vertical bar space equals space minus left parenthesis 3 minus 3 right parenthesis space equals space 0 space space space space space straight A subscript 33 space equals space open vertical bar table row 1 cell space space space 3 end cell row 1 cell space space space 4 end cell end table close vertical bar space equals space 4 minus 3 space equals space 1 space space space space space space adj. space straight A space equals space open square brackets table row cell straight A subscript 11 end cell cell space space straight A subscript 12 end cell cell space space space space straight A subscript 13 end cell row cell straight A subscript 12 end cell cell straight A subscript 22 end cell cell space space straight A subscript 23 end cell row cell straight A subscript 31 end cell cell straight A subscript 32 end cell cell space space straight A subscript 33 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row 7 cell space space space minus 1 end cell cell space space space minus 1 end cell row cell negative 3 end cell cell space space space space space 1 end cell cell space space space space space space 0 end cell row cell negative 3 end cell cell space space space space 0 end cell cell space space space space space 1 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row 7 cell space space minus 3 end cell cell space space minus 3 end cell row cell negative 1 end cell 1 cell space space space 0 end cell row cell negative 1 end cell 0 cell space space space 1 end cell end table close square brackets Now space space space space straight A left parenthesis adj space straight A right parenthesis space equals space open square brackets table row 1 cell space space 3 end cell cell space space space 3 end cell row 1 cell space space 4 end cell cell space space 3 end cell row 1 cell space space 3 end cell cell space space space 4 end cell end table close square brackets space space open square brackets table row cell space space space 7 end cell cell space space minus 3 end cell cell space space space minus 3 end cell row cell negative 1 end cell cell space space space space space 1 end cell cell space space space space space space 0 end cell row cell negative 1 end cell cell space space space space 0 end cell cell space space space space space 1 end cell end table close square brackets

equals space open square brackets table row cell 7 minus 3 minus 3 end cell cell space space space minus 3 plus 3 plus 0 end cell cell space space minus 3 plus 0 plus 3 end cell row cell 7 minus 4 minus 3 end cell cell space space minus 3 plus 4 plus 0 end cell cell space space minus 3 plus 0 plus 3 end cell row cell 7 minus 3 minus 4 end cell cell space minus 3 plus 3 plus 0 end cell cell space space space minus 3 plus 0 plus 4 end cell end table close square brackets space equals space open square brackets table row 1 cell space space 0 end cell cell space space space 0 end cell row 0 cell space space 1 end cell cell space space space 0 end cell row 0 cell space space 0 end cell cell space space space 1 end cell end table close square brackets space equals space left parenthesis 1 right parenthesis space open square brackets table row 1 cell space space 0 end cell cell space space 0 end cell row 0 cell space space 1 end cell cell space space 0 end cell row 0 cell space space 0 end cell cell space space 1 end cell end table close square brackets space equals space open vertical bar straight A close vertical bar space straight I therefore space space space space space straight A left parenthesis adj space straight A right parenthesis space space equals open vertical bar straight A close vertical bar space space straight I Now space space space space space space space space space space space straight A to the power of negative 1 end exponent space equals space fraction numerator 1 over denominator open vertical bar straight A close vertical bar end fraction space adj space straight A space equals space 1 over 1 open square brackets table row 7 cell space space space minus 3 end cell cell space space minus 3 end cell row cell negative 1 end cell cell space space space space space 1 end cell cell space space space space space 0 end cell row cell negative 1 end cell cell space space space space space space space 0 space end cell cell space space space space 1 end cell end table close square brackets space equals space open square brackets table row cell space space 7 end cell cell space space space minus 3 end cell cell space space minus 3 end cell row cell negative 1 end cell cell space space space space space space 1 end cell cell space space space space space 0 end cell row cell negative 1 end cell cell space space space space space space 0 end cell cell space space space space space 1 end cell end table close square brackets

86 Views

Short Answer Type

203.

Find the inverse of the matrix $open square brackets table row 1 cell space space 2 end cell cell space space 3 end cell row 0 cell space space 2 end cell cell space space 4 end cell row 0 cell space space 0 end cell cell space space 5 end cell end table close square brackets$ .

76 Views

Long Answer Type

204.

Find the inverse of the matrix $open square brackets table row 1 cell space space space space 0 end cell cell space space space space 0 end cell row 3 cell space space space 3 end cell cell space space space space space 0 end cell row 5 cell space space space space 2 end cell cell space space minus 1 end cell end table close square brackets$

73 Views

205.

Find the inverse of the matrix:
$open square brackets table row 2 cell space space space space space 1 end cell cell space space space space space 3 end cell row 4 cell space minus 1 end cell cell space space space space space 0 end cell row cell negative 7 end cell cell space space space space space 2 end cell cell space space space space 1 end cell end table close square brackets$

74 Views

206.

Find the inverse of the matrix:
$open square brackets table row cell space space space 2 end cell cell space space space space minus 1 end cell cell space space space space space 1 end cell row cell negative 1 end cell cell space space space space space space space 2 end cell cell space space minus 1 end cell row cell space space 1 end cell cell space space space space minus 1 end cell cell space space space space space 2 end cell end table close square brackets$

75 Views

Short Answer Type

207.

Find the inverse of the matrix:
$open square brackets table row 2 cell space space minus 3 end cell cell space space space space 3 end cell row 3 cell space space space space space 2 end cell cell space space space space space 3 end cell row 3 cell space space minus 2 end cell cell space space space space 2 end cell end table close square brackets$

72 Views

Long Answer Type

208.

Find the inverse of the matrix:
$open square brackets table row 1 cell space space 2 end cell cell space space 2 end cell row 2 cell space 1 end cell cell space 2 end cell row 2 cell space 2 end cell cell space 1 end cell end table close square brackets$

82 Views

209.

Find the inverse of the matrix:
$open square brackets table row 1 cell space 0 end cell cell space 0 end cell row 0 cell space space cos space straight alpha end cell cell space space sin space straight alpha end cell row 0 cell space sin space straight alpha end cell cell space space minus cos space straight alpha end cell end table close square brackets$

74 Views

210.

If $straight A space equals space open square brackets table row 1 cell space 2 end cell cell space space 5 end cell row 2 cell space 3 end cell cell space 1 end cell row cell negative 1 end cell cell space 1 end cell cell space 1 end cell end table close square brackets comma$ then compute the inverse of A and verify that A^–1 A = I = A A^–1

75 Views

Previous Year Papers

Test Series

Test Yourself

Long Answer Type

202. If then verify that A adj A = | A | I. Also find A .

Short Answer Type

Long Answer Type

Short Answer Type

Long Answer Type