Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 3>Q 10

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Let $A$ and $B$ be $3 \times 3$ matrices such that $A B + A + B = 0$ , then

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Important Questions on Matrices and Determinants

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 18

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:

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 3>Q 11

|A - B| \neq 0, A^{4} = B^{4}, C^{3} A = C^{3} B, B^{3} A = A^{3} B,

then

|A^{3} + B^{3} + C^{3}| =

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 3>Q 12

Let

A = [\begin{array}{l} 1 & 1 \\ 0 & 1 \end{array}]

and

B = [\begin{array}{l} b_{1} & b_{2} \\ b_{3} & b_{4} \end{array}]

. If

10 A^{10} + adj (A^{10}) = B

, then

b_{1} + b_{2} + b_{3} + b_{4}

is equal to

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 3>Q 13

The matrices

P = [\begin{array}{l} u_{1} & v_{1} & w_{1} \\ u_{2} & v_{2} & w_{2} \\ u_{3} & v_{3} & w_{3} \end{array}]

,

Q = \frac{1}{9} [\begin{array}{rcc} 2 & 2 & 1 \\ - 12 & 5 & m \\ - 8 & 1 & 5 \end{array}]

are such that

P Q = I

and

[\begin{array}{l} u_{1} & v_{1} & w_{1} \\ u_{2} & v_{2} & w_{2} \\ u_{3} & v_{3} & w_{3} \end{array}] [\begin{array}{l} x \\ y \\ z \end{array}] = [\begin{array}{l} 1 \\ 1 \\ 5 \end{array}] .

If

y = - 3,

then the value of

m,

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 3>Q 14

Statement

I

: Suppose

A = [\begin{array}{l} 1 & π \\ 0 & 1 \end{array}],

then

A^{100} = [\begin{matrix} 1 & 100 π \\ 0 & 1 \end{matrix}]

Statement II: Suppose

B

is a

2 \times 2

matrix such that

B^{2} = 0,

then

(I + B)^{n} = I + n B

for each

n \in N .

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 3>Q 15

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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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 3>Q 17

If

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

then the value of

det (A^{4}) + det (A^{10} - (Adj (2 A))^{10})

is equal to ________.

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 3>Q 18

Let

A = \{a_{i j}\}

be a

3 \times 3

matrix, where

a_{i j} = \{\begin{matrix} {(- 1)}^{j - i} if i < j \\ 2 if i = j \\ {(- 1)}^{i + j} if i > j \end{matrix}

then

\det (3 Adj (2 A^{- 1}))

is equal to ________.