Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 39

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

$A$ and $B$ are two $3 \times 3$ matrices such that they are inverse of each other then $t r . (5 A B + 6 B A + 7 {(A B)}^{2} + 8 {(B A)}^{2})$ is equal to

50% studentsanswered this correctly

Important Questions on Matrices

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 40

If

A

and

B

are orthogonal matrices of order

4 \times 4

and

5 \times 5

respectively then

t r . (A A^{T} + 2 A^{T} A + 5 (A A^{T}) + t r . (2 B B^{T} + 4 B^{T} B))

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 41

Let

A = [\begin{matrix} 3 & 1 \\ - 16 & - 5 \end{matrix}]

, then the sum of all the elements of

A^{50}

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 43

If

3 A = [\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ x & 2 & y \end{matrix}]

and

A^{T} A = A A^{T} = I,

then

x y

is equal to

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 44

Let

A = [\begin{matrix} - 5 & - 8 & 0 \\ 3 & 5 & 0 \\ 1 & 2 & - 1 \end{matrix}]

and

B = A + A^{2} + A^{4} + A^{8} + . . . . + A^{2^{78}}

then sum of all the elements of matrix

B

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 1

If

A, B

and

A + B

are idempotent matrices, then

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 2

Let $t$ be the trace of the matrix

$A = [\begin{matrix} \frac{|x + y|}{|x| + |y|} & α_{1} & β_{1} \\ α_{2} & \frac{|y + z|}{|y| + |z|} & β_{2} \\ α_{3} & β_{3} & \frac{|z + x|}{|z| + |x|} \end{matrix}],$ then

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 3

Let

A

be an involutory matrix and

S

be the set containing solution of

A^{x} = I

. Then minimum value of

\sum_{x \in S}^{\infty} (\sin^{x} θ + \cos^{x} θ)

(Given that

x \in N

).

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 19 - Matrices>Assignment>Q 5

An orthogonal matrix is