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.

Matrices

Short Answer Type

101. $If space straight A equals open square brackets table row 2 cell space minus 1 end cell row 3 cell space space space space 1 end cell end table close square brackets space comma space straight B equals space open square brackets table row 1 cell space space 3 end cell row 2 cell space 1 end cell end table close square brackets$ verify that (A + B) (A – B) ≠ A² – B².

Here space straight A equals space open square brackets table row 2 cell space minus 1 end cell row 3 cell space space space space space space 1 end cell end table close square brackets space comma space straight B equals open square brackets table row 1 cell space space 3 end cell row 2 cell space space 1 end cell end table close square brackets therefore space straight A plus straight B space equals space open square brackets table row cell 2 plus 1 end cell cell space minus 1 plus 3 end cell row cell 3 plus 2 end cell cell space space space space space 1 plus 1 end cell end table close square brackets space equals space open square brackets table row 3 cell space space space 2 end cell row 5 cell space space 2 end cell end table close square brackets space space straight A minus straight B space equals open square brackets table row cell 2 minus 1 end cell cell space minus 1 minus 3 end cell row cell 3 minus 2 end cell cell space space space space space 1 minus 1 end cell end table close square brackets equals open square brackets table row 1 cell space minus 4 end cell row 1 cell space space space space 0 end cell end table close square brackets therefore space left parenthesis straight A plus straight B right parenthesis left parenthesis straight A minus straight B right parenthesis space equals space open square brackets table row cell 3 space end cell cell space space space 2 end cell row 5 cell space space 2 end cell end table close square brackets space open square brackets table row 1 cell space minus 4 end cell row 1 cell space space space space space 0 end cell end table close square brackets equals open square brackets table row cell 3 plus 2 end cell cell space space minus 12 plus 0 end cell row cell 5 plus 2 end cell cell space space space minus 20 plus 0 end cell end table close square brackets equals open square brackets table row 5 cell space space minus 12 end cell row 7 cell space space minus 20 end cell end table close square brackets space... left parenthesis 1 right parenthesis space space space straight A to the power of 2 minus end exponent straight B squared space equals space open square brackets table row 2 cell space space minus 1 end cell row 3 cell space space space space space space space 1 end cell end table close square brackets space open square brackets table row 2 cell space minus 1 end cell row 3 cell space space space space 1 end cell end table close square brackets minus open square brackets table row 1 cell space space 3 end cell row 2 cell space space 1 end cell end table close square brackets space space space space space space space space space space space space space space equals open square brackets table row cell 4 minus 3 end cell cell negative 2 minus 1 end cell row cell 6 plus 3 end cell cell negative 3 plus 1 end cell end table close square brackets minus open square brackets table row cell 1 plus 6 end cell cell 3 plus 3 end cell row cell 2 plus 2 end cell cell 6 plus 1 end cell end table close square brackets space space space space space space space space space space space space space space equals space open square brackets table row 1 cell negative 3 end cell row 9 cell negative 2 end cell end table close square brackets minus open square brackets table row 7 6 row 4 7 end table close square brackets equals open square brackets table row cell 1 minus 7 end cell cell negative 3 minus 6 end cell row cell 9 minus 4 end cell cell negative 2 minus 7 end cell end table close square brackets equals open square brackets table row cell negative 6 end cell cell negative 9 end cell row 5 cell negative 9 end cell end table close square brackets space... left parenthesis 2 right parenthesis space space space space space space space space space space space space space From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space left parenthesis straight A space plus space straight B right parenthesis space left parenthesis straight A space – space straight B right parenthesis space not equal to space straight A squared space – space straight B squared

94 Views

102.

If space straight A equals open square brackets table row 0 cell space space space 0 end cell cell space space 1 end cell row 0 cell space space 1 end cell cell space space 0 end cell row 1 cell space space 0 end cell cell space space 0 end cell end table close square brackets space comma

find A². Hence find the matrix A⁶.

76 Views

103.

IF space matrix space straight A equals open square brackets table row 0 cell space 0 end cell row 4 cell space 0 end cell end table close square brackets

,find A¹⁶

131 Views

104.

if space open square brackets table row 1 0 row 0 1 end table close square brackets comma space straight A equals open square brackets table row 0 1 row 0 0 end table close square brackets comma space then space show space that left parenthesis straight a space straight I space plus straight b space straight A right parenthesis cubed equals straight a cubed straight I plus 3 space straight a squared space bA.

74 Views

105. Solve for x and y, given that

open square brackets table row 3 cell space space minus 4 end cell row 1 cell space space space space space 2 end cell end table close square brackets space open square brackets table row x row y end table close square brackets equals open square brackets table row cell space 3 end cell row 11 end table close square brackets

77 Views

106. Solve for.x and y, given that

open square brackets table row x y row cell 3 y end cell x end table close square brackets open square brackets table row 1 row 2 end table close square brackets equals open square brackets table row 3 row 5 end table close square brackets

88 Views

107.

Solve space for space straight x space andy comma space given space that open square brackets table row 2 cell negative 3 end cell row 1 1 end table close square brackets space open square brackets table row straight x row straight y end table close square brackets equals open square brackets table row 1 row 3 end table close square brackets

75 Views

108.

Find space the space values space of space straight a space and space straight b space for space which space the space following space holds space colon open square brackets table row straight a straight b row cell negative straight a end cell cell 2 straight b end cell end table close square brackets space open square brackets table row 2 row cell negative 1 end cell end table close square brackets equals open square brackets table row 5 row 4 end table close square brackets

74 Views

109.

Find space the space values space of space straight a space and space straight b space for space which space the space following space holds space colon open square brackets table row 4 2 row 3 cell negative 1 end cell end table close square brackets space open square brackets table row straight a row straight b end table close square brackets equals space open square brackets table row cell negative 4 end cell row 2 end table close square brackets

74 Views

110.

Let space straight A equals open square brackets table row 2 cell negative 1 end cell row 3 4 end table close square brackets straight B equals space open square brackets table row 5 2 row 7 4 end table close square brackets comma space straight C equals space open square brackets table row 2 5 row 3 8 end table close square brackets space Find space straight a space matrix space straight D space such space that space CD minus AB equals 0

74 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

101. verify that (A + B) (A – B) ≠ A2 – B2.