EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Matrices and Determinants>JEE Advanced Paper 1 - 2019>Q 16

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

Let $S$ be the sample space of all $3 \times 3$ matrices with entries from the set $\{0, 1\} .$ Let the events $E_{1}$ and $E_{2}$ be given by $E_{1} = \{A \in S : d e t A = 0\}$ and $E_{2} = {A \in S :$ sum of entries of $A$ is $7} .$ If a matrix is chosen at random from $S,$ then the conditional probability $P (E_{1}| E_{2})$ equals____

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Important Questions on Matrices and Determinants

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Matrices and Determinants>JEE Advanced Paper 1 - 2017>Q 17

Which of the following is (are) NOT the square of a

3 \times 3

matrix with real entries?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Matrices and Determinants>JEE Advanced Paper 1 - 2016>Q 19

Let

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

, where

α \in R,

Suppose

Q = [q_{i j}]

is a matrix such that

P Q = k I

, where

k \in R, k \neq0

and

I

is the identity matrix of order

3

. If

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

and

\det (Q) = \frac{k^{2}}{2}

then

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Matrices and Determinants>JEE Advanced Paper 1 - 2015>Q 21

Let

X a n d Y

be two arbitrary,

3 \times 3

, non - zero, skew - symmetric matrices and Z be an arbitrary

3 \times 3

, non - zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric ?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Matrices and Determinants>JEE Advanced Paper 1 - 2015>Q 22

Which of the following values of

α

satisfy the equation

|\begin{matrix} {(1 + α)}^{2} & {(1 + 2 α)}^{2} & {(1 + 3 α)}^{2} \\ {(2 + α)}^{2} & {(2 + 2 α)}^{2} & {(2 + 3 α)}^{2} \\ {(3 + α)}^{2} & {(3 + 2 α)}^{2} & {(3 + 3 α)}^{2} \end{matrix}| = - 648 α

?

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Matrices and Determinants>JEE Advanced Paper 1 - 2014>Q 23

Let

M

be a

2 \times 2

symmetric matrix with integer entries. Then

M

is invertible if

HARD

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Matrices and Determinants>JEE Advanced Paper 1 - 2014>Q 24

Let

M

and

N

be two

3 \times 3

matrices such that

M N = N M

. Further, if

M \neq N^{2}

and

M^{2} = N^{4}

, then

MEDIUM

JEE Advanced

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 7 - Matrices and Determinants>JEE Advanced Paper 1 - 2013>Q 25

For

3 \times 3

matrices

M

and

N

, which of the following statement(s) is (are) NOT correct?