Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 76

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Let $A = [\begin{array}{l} a & 0 & b \\ 1 & e & 1 \\ c & 0 & d \end{array}] [\begin{array}{l} x \\ y \\ z \end{array}] = [\begin{array}{l} 0 \\ 0 \\ 0 \end{array}],$ where $a, b, c, d, e \in \{0, 1\},$ then number of such matrix $A$ for which system of equation $A X = 0$ have unique solution.

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Important Questions on Matrices and Determinants

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-1>Q 77

If the system of equations

a x + y + z = 0, x + b y + z = 0

and

x + y + c z = 0

(a, b, c \neq 1)

has a non-trivial solution, then the value of

\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 1

Two matrices

A

and

B

have in total

6

different elements (none repeated). How many matrices

A

and

B

are possible such that product

A B

is defined.

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 2

If

A B = O

for the matrices

A = [\begin{matrix} \cos^{2} θ & \cos θ \sin θ \\ \cos θ \sin θ & \sin^{2} θ \end{matrix}]

and

B = [\begin{matrix} \cos^{2} ϕ & \cos ϕ \sin ϕ \\ cosϕ \sin ϕ & \sin^{2} ϕ \end{matrix}]

, then

θ - ϕ

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 3

If

X = [\begin{array}{l} 3 & - 4 \\ 1 & - 1 \end{array}],

then value of

X^{n}

is, (where

n

is natural number)

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 4

A

and

B

are two matrices such that

A B = B, B A = A

then

A^{2} + B^{2} =

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 5

Find the number of all possible ordered sets of two

(n \times n)

matrices

A

and

B

for which

A B - B A = I

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 6

If

B, C

are square matrices of order

n

and if

A = B + C, B C = C B, C^{2} = O,

then which of following is true for any positive integer

N .

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Alpha Question Bank for Engineering: Mathematics>Chapter 9 - Matrices and Determinants>Exercise-2>Q 7

How many

3 \times 3

skew-symmetric matrices can be formed using numbers

- 2, - 1, 1, 2, 3, 4, 0

(any number can be used any number of times but

0

can be used at most

3

times)