Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Work Book Exercise 2.2>Q 9

EASY

JEE Advanced

IMPORTANT

Earn 100

The system of equations $2 x - y + z = 0$ $, x - 2 y + z = 0$ and $λ x - y + 2 z = 0$ has infinite number of non-trivial solution for

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Important Questions on Determinant

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 1

If

A

is a square matrix such that

A^{2} = A,

then

|A|

equals

EASY

JEE Advanced

IMPORTANT

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

If

A

is a square matrix such that

|A| = 2,

then for any positive integer

n, | A |^{n}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 3

If each element of

3 \times 3

matrix is multiplied by

3

, then the determinant of the newly formed matrix is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 4

The value of determinant

|\begin{matrix} 1 & 1 & 1 \\ e & π & \sqrt{2} \\ 2 & 2 & 2 \end{matrix}|

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 5

The value of determinant

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

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 6

The value of determinant

|\begin{array}{l} a_{1} & l a_{1} + m b_{1} & b_{1} \\ a_{2} & l a_{2} + m b_{2} & b_{2} \\ a_{3} & l a_{3} + m b_{3} & b_{3} \end{array}|

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 7

The value of determinant

|\begin{matrix} 1 + a & 1 & 1 \\ 1 & 1 + a & 1 \\ 1 & 1 & 1 + a \end{matrix}|

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 2 - Determinant>Target Exercises>Q 8

The value of the determinant

|\begin{array}{l} a - b & b - c & c - a \\ x - y & y - z & z - x \\ p - q & q - r & r - p \end{array}|

is