NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 34

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IMPORTANT

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If $A$ and $B$ are invertible matrices, then which of the following is not correct?

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Important Questions on Determinants

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12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 35

If

x, y, z

are all different from zero and

|\begin{matrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{matrix}| = 0

, then value of

x^{- 1} + y^{- 1} + z^{- 1}

is

EASY

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 36

The value of the determinant

|\begin{matrix} x & x + y & x + 2 y \\ x + 2 y & x & x + y \\ x + y & x + 2 y & x \end{matrix}|

is

EASY

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 37

There are two values of

a

which makes determinant,

Δ = |\begin{matrix} 1 & - 2 & 5 \\ 2 & a & - 1 \\ 0 & 4 & 2 a \end{matrix}| = 86

, then sum of these number is

EASY

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 38

If

A

is a matrix of order

3 \times 3

, then

| 3 A | =

_____

| A |

EASY

12th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 39

If

A

is invertible matrix of order

3 \times 3

, then

| A | |A^{- 1}|

is _____.

EASY

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 40

If

x, y, z \in R

, then the value of determinant

|\begin{array}{l} {(2^{x} + 2^{- x})}^{2} & {(2^{x} - 2^{- x})}^{2} & 1 \\ {(3^{x} + 3^{- x})}^{2} & {(3^{x} - 3^{- x})}^{2} & 1 \\ {(4^{x} + 4^{- x})}^{2} & {(4^{x} - 4^{- x})}^{2} & 1 \end{array}|

is equal to _____.

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NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 41

If

\cos 2 θ = 0

and

{|\begin{matrix} 0 & \cos θ & \sin θ \\ \cos θ & \sin θ & 0 \\ \sin θ & 0 & \cos θ \end{matrix}|}^{2} = \frac{k}{2}

, then the value of

k =

_____.

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IMPORTANT

NCERT Exemplar Mathematics - Class 12>Chapter 4 - Determinants>EXERCISE>Q 42

If

A

is a matrix of order

3 \times 3

, then

{(A^{2})}^{- 1} = {(A^{- 1})}^{k}

,

k =

_____.