EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 17 March 2021 Shift 2>Q 39

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If $x, y, z$ are in arithmetic progression with common difference $d, x \neq 3 d,$ and the determinant of the matrix $[\begin{matrix} 3 & 4 \sqrt{2} & x \\ 4 & 5 \sqrt{2} & y \\ 5 & k & z \end{matrix}]$ is zero, then the value of $k^{2}$ is

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Important Questions on Matrices and Determinants

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 18 March 2021 Shift 1>Q 43

Let

A + 2 B = [\begin{matrix} 1 & 2 & 0 \\ 6 & - 3 & 3 \\ - 5 & 3 & 1 \end{matrix}]

and

2 A - B = [\begin{matrix} 2 & - 1 & 5 \\ 2 & - 1 & 6 \\ 0 & 1 & 2 \end{matrix}] .

If

T r (A)

denotes the sum of all diagonal elements of the matrix

A,

then

Tr (A) - Tr (B)

has value equal to

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main 18 March 2021 Shift 2>Q 45

Let

I

be an identity matrix of order

2 \times 2

and

P = [\begin{matrix} 2 & - 1 \\ 5 & - 3 \end{matrix}]

. Then the value of

n \in N

for which

P^{n} = 5 I - 8 P

is equal to ___ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 24 Feb 2021 Shift 1>Q 47

Let

P = [\begin{array}{r} 3 & - 1 & - 2 \\ 2 & 0 & α \\ 3 & - 5 & 0 \end{array}],

where

α \in R .

Suppose

Q = [q_{i j}]

is a matrix satisfying

P Q = k I_{3}

for
some non-zero

k \in R .

If

q_{23} = - \frac{k}{8}

and

|Q| = \frac{k^{2}}{2}

, then

α^{2} + k^{2}

is equal to_________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 24 Feb 2021 Shift 1>Q 48

Let

M

be any

3 \times 3

matrix with entries from the set

\{0, 1, 2\}

. The maximum number of such matrices, for which the sum of diagonal elements of

M^{T} M

is seven, is______.

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JEE Main

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 25 Feb 2021 Shift 1>Q 52

Let

A = [\begin{array}{l} x & y & z \\ y & z & x \\ z & x & y \end{array}],

where

x, y

and

z

are real numbers such that

x + y + z > 0

and

x y z = 2

. If

A^{2} = I_{3}

, then the value of

x^{3} + y^{3} + z^{3}

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 25 Feb 2021 Shift 1>Q 53

If the system of equations

$k x + y + 2 z = 1$

$3 x - y - 2 z = 2$

$- 2 x - 2 y - 4 z = 3$

has infinitely many solutions, then $k$ is equal to ______ .

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 25 Feb 2021 Shift 2>Q 55

If for the matrix,

A = [\begin{matrix} 1 & - α \\ α & β \end{matrix}], A A^{T} = I_{2}

, then the value of

α^{4} + β^{4}

is :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 8 - Matrices and Determinants>JEE Main - 26 Feb 2021 Shift 1>Q 57

Let

A

be a symmetric matrix of order

2

with integer entries. If the sum of the diagonal elements of

A^{2}

is

1,

then the possible number of such matrices is: