Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 37

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IMPORTANT

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If $A$ is an invertible matrix, then

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Important Questions on Determinant

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 38

If

n^{th}

order square matrix

A

is an orthogonal, then

|adj (adj A)|

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 39

If

A = [\begin{array}{l} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{array}],

then the value of

|A| |adj A|

is

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 41

If

A

is singular matrix, then

A \cdot (adj A)

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 42

If

A^{'}

is the transpose of a square matrix

A

, then

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 43

If

A = [\begin{matrix} a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a \end{matrix}],

then the value of

|adj A|

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 44

If the system of equations

a x + y + z = 0, x + b y + z = 0

and

x + y + c z = 0

(a, b, c \neq 1)

has a non-trivial solution, then the value of

\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}

is

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 45

In a third order of determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then, it can be decomposed into