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Determinants

Long Answer Type

231.

Examine the consistency of the system of equations:
3x – y – 2z = 2
2y – z = – 1
3x – 5y = 3

80 Views

Short Answer Type

232.

Examine the consistency of the system of equations:
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = – 1

90 Views

Long Answer Type

233.

Examine the consistencies of the system of equations:
3x – y + 2z = 3
2x + y + 3z =5
x - 2y - z = 1

91 Views

234.

Examine the consistencies of the system of equations:
x - y+ z = 3
2x - y – z = 2
– x – 2y + 2z = 1

74 Views

Short Answer Type

235. Solve the following system of equations using matrix method:
2x + 5y = 1
1x + 2y = 7

The given equations are
2x + 5y = 1
3x + 2y = 7
These equations can be written as
$open square brackets table row 2 cell space space 5 end cell row 3 cell space space 2 end cell end table close square brackets space open square brackets table row straight x row straight y end table close square brackets space equals space open square brackets table row 1 row 7 end table close square brackets$
or $AX space equals space straight B space space space space where space straight A space equals space open square brackets table row 2 cell space space space 5 end cell row 3 cell space space 2 end cell end table close square brackets comma space space space straight X space equals open square brackets table row straight x row straight y end table close square brackets comma space space space straight B space equals space open square brackets table row 1 row 7 end table close square brackets space$
$open vertical bar straight A close vertical bar space equals space open vertical bar table row 2 cell space space space 5 end cell row 3 cell space space space 2 end cell end table close vertical bar space equals space 4 minus 15 space equals space minus 11 space not equal to space 0 therefore space space space straight A to the power of negative 1 end exponent space exists space space space space space space space straight A subscript 11 space equals space 2 comma space space space straight A subscript 12 space equals negative 3 comma space space space straight A subscript 21 space equals space minus 5 comma space space straight A subscript 22 space equals space 2 space space space space space space space adj. space straight A space equals space open square brackets table row 2 cell space space space minus 3 end cell row cell negative 5 end cell cell space space space space space space 2 end cell end table close square brackets to the power of apostrophe space equals space open square brackets table row cell space space 2 end cell cell space space space minus 5 end cell row cell negative 3 end cell cell space space space space space space space 2 end cell end table close square brackets space space space space space space space space space space space space space space space space straight A to the power of negative 1 end exponent space equals space fraction numerator adj. space straight A over denominator open vertical bar straight A close vertical bar end fraction space equals negative 1 over 11 open square brackets table row 2 cell space space space minus 5 end cell row cell negative 3 end cell cell space space space space space 2 end cell end table close square brackets Now space AX space equals space straight B space space space space space rightwards double arrow space space space space straight X space equals space straight A to the power of negative 1 end exponent straight B$

$rightwards double arrow space space space space space open square brackets table row straight x row straight y end table close square brackets space equals space minus 1 over 11 open square brackets table row 2 cell space space minus 5 end cell row cell negative 3 end cell cell space space space space 2 end cell end table close square brackets space open square brackets table row 1 row 7 end table close square brackets space space space space space rightwards double arrow space space space open square brackets table row straight x row straight y end table close square brackets space equals space minus 1 over 11 open square brackets table row cell space 2 minus 35 end cell row cell negative 3 plus 14 end cell end table close square brackets rightwards double arrow space space space space open square brackets table row straight x row straight y end table close square brackets space equals space minus 1 over 11 open square brackets table row cell negative 33 end cell row 11 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space open square brackets table row straight x row straight y end table close square brackets space equals space open square brackets table row cell space space space space 3 end cell row cell negative 1 end cell end table close square brackets therefore space space space space space straight x space equals space 3 comma space space space space space straight y space equals space minus 1.$