Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 12

MEDIUM

JEE Main

IMPORTANT

Earn 100

$A, B, C$ are three matrices of the same order such that any two are symmetric and the $3^{rd}$ one is skew-symmetric. If $X = A B C + C B A$ and $Y = A B C - C B A,$ then ${(X Y)}^{T}$ is

15.91% studentsanswered this correctly

Important Questions on Matrices

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 13

If

A

and

P

are different matrices of order

n

, satisfying

A^{3} = P^{3}

and

A^{2} P = P^{2} A

(where

| A - P | \neq 0

) then

|A^{2} + P^{2}|

is equal to

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 1

Let

A, B

are square matrices of same order satisfying

A B = A

and

B A = B

then

{(A^{2010} + B^{2010})}^{2011}

equals

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 2

The number of

2 \times 2

matrices

A

, that are there with the elements as real numbers satisfying

A + A^{T} = I

and

A A^{T} = I

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 3

If the orthogonal square matrices

A

and

B

of same order satisfy

\det A + \det B = 0

, then the value of

\det (A + B)

is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 4

If

A = [\begin{matrix} \cos θ & \sin θ \\ \sin θ & - \cos θ \end{matrix}], B = [\begin{matrix} 1 & 0 \\ - 1 & 1 \end{matrix}], C = A B A^{T}

, then

A^{T} C^{n} A

,

n \in I^{+}

equals to

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 5

Let

A

be a

3 \times 3

matrix given by

A = {(a_{i j})}_{3 \times 3}

. If for every column, vector

X

satisfies

X^{'} A X = 0

and

a_{12} = 2008, a_{13} = 2010

and

a_{23} = - 2012

, then the value of

a_{21} + a_{31} + a_{32}

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 6

A

and

B

are two non-singular matrices such that

A^{6} = I

and

B A = A B^{2}

, find the value of

k

so that

B^{k} = I

is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 7

Let

A

be a

2 \times 3

matrix, while

B

be a

3 \times 2

matrix. If

|A B| = 4

, then the value of

|B A|

is