EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 4th April 2015>Q 145

HARD

JEE Main

IMPORTANT

Earn 100

The set of all values of $λ$ for which the system of linear equations:
$2 x_{1} - 2 x_{2} + x_{3} = λ x_{1}$
$2 x_{1} - 3 x_{2} + {2 x}_{3} = λ x_{2}$
$- x_{1} + {2 x}_{2} = λ x_{3}$
has a non-trivial solution,

66.67% studentsanswered this correctly

Important Questions on Matrices and Determinants

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 11th April 2015>Q 146

If

A

is a

3 \times 3

matrix such that

|5 a d j A| = 5

, then

|A|

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 11th April 2015>Q 147

If

|\begin{matrix} x^{2} + x & x + 1 & x - 2 \\ 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 \\ x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix}| = a x - 12

, then

a

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 19th April 2014>Q 148

If

Δ_{r} = |\begin{matrix} r & 2 r - 1 & 3 r - 2 \\ \frac{n}{2} & n - 1 & a \\ \frac{1}{2} n (n - 1) & {(n - 1)}^{2} & \frac{1}{2} (n - 1) (3 n + 4) \end{matrix}|

, then the value of

\sum_{r = 1}^{n - 1} Δ_{r}

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 19th April 2014>Q 149

Let

A

and

B

be any two

3 \times 3

matrices. If

A

is symmetric and

B

is skew symmetric, then the matrix

A B - B A

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 9th April 2014>Q 150

If $a, b, c$ are non - zero real numbers and if the system of equations

$(a - 1) x = y + z$

$(b - 1) y = x + z$

$(c - 1) z = x + y$

has a non - trivial solution, then $a b + b c + c a$ equals :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 9th April 2014>Q 151

If $B$ is a $3 \times 3$ matrix such that $B^{2} = 0$ , then $d e t . [{(I + B)}^{50} - 50 B]$ is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 6th April 2014>Q 152

If

α, β \neq 0

,

f (n) = α^{n} + β^{n}

and

|\begin{matrix} 3 & 1 + f (1) & 1 + f (2) \\ 1 + f (1) & 1 + f (2) & 1 + f (3) \\ 1 + f (2) & 1 + f (3) & 1 + f (4) \end{matrix}| = K {(1 - α)}^{2} {(1 - β)}^{2} {(α - β)}^{2}

, then

K

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 6th April 2014>Q 153

If

A

is a

3 \times 3

non-singular matrix such that

A A^{'} = A^{'} A

and

B = A^{- 1} A^{'},

then

B B^{'}

equals, where

X^{'}

denotes the transpose of the matrix

X

.