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

HARD

JEE Main

IMPORTANT

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Let $A, B$ are square matrices of same order satisfying $A B = A$ and $B A = B$ then ${(A^{2010} + B^{2010})}^{2011}$ equals

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Important Questions on Matrices

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

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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

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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

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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

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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

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 9 - Matrices>DPP>Q 8

Let

A

be a square matrix of order

3

, so that sum of elements of each row is

1

. Then, the sum of elements of matrix

A^{2}

is

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JEE Main

IMPORTANT

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

Let

A

and

B

be

3 \times 3

matrices such that

A B + A + B = 0

, then