Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 8

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If $I_{3}$ is the identity matrix of order $3,$ then $I_{3}^{- 1}$ is -

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Important Questions on Determinants

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 9

Inverse of the matrix

[\begin{matrix} \cos 2 θ - \sin 2 θ \\ \sin 2 θ \cos 2 θ \end{matrix}] i s

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 10

A = [\begin{array}{l} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & - 2 & 4 \end{array}], I = [\begin{array}{l} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]

,

A^{- 1} = \frac{1}{6} (A^{2} + c A + d I)

where

c, d \in R,

then pair of values

(c, d)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 11

x + k y - z = 0, 3 x - k y - z = 0

and

x - 3 y + z = 0

has non-zero solution for

k =

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 12

If

a_{1} x + b_{1} y + c_{1} z = 0, a_{2} x + b_{2} y + c_{2} z = 0, a_{3} x + b_{3} y + c_{3} z = 0

and

|\begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix}| = 0

, then the given system has -

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 13

The existence of the unique solution of the system

x + y + z = λ, 5 x - y + μ z = 10, 2 x + 3 y - z = 6

depends -

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 14

The value of

λ

for which the system of equations

2 x - y - z = 12, x - 2 y + z = - 4, x + y + λ z = 4

has no solution is -

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 15

The number of solution of the following equations

x_{2} - x_{3} = 1, - x_{1} + 2 x_{3} = - 2, x_{1} - 2 x_{2} = 3

is-

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>EXERCISE>Q 16

The solution of the equation

[\begin{matrix} 1 & 0 & 1 \\ - 1 & 1 & 0 \\ 0 & - 1 & 1 \end{matrix}] [\begin{array}{l} x \\ y \\ z \end{array}] = [\begin{array}{l} 1 \\ 1 \\ 2 \end{array}]

is

(x, y, z) =