Mathematics>Algebra>Matrices>Types of Matrices

EASY

Earn 100

Define comparable matrices.

Important Questions on Matrices

EASY

Mathematics>Algebra>Matrices>Types of Matrices

The trace of the matrix

A = [\begin{matrix} 1 & - 5 & 7 \\ 0 & 7 & 9 \\ 11 & 8 & 9 \end{matrix}]

is

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Mathematics>Algebra>Matrices>Types of Matrices

The determinant of a square null matrix of order

3

is _____

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Mathematics>Algebra>Matrices>Types of Matrices

If

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

and

A^{- 1} = [\begin{matrix} \frac{1}{2} & \frac{- 1}{2} & \frac{1}{2} \\ - 4 & 3 & c \\ \frac{5}{2} & \frac{- 3}{2} & \frac{1}{2} \end{matrix}]

then

EASY

Mathematics>Algebra>Matrices>Types of Matrices

A = {[a_{i j}]}_{m \times n}

is a square matrix, if

EASY

Mathematics>Algebra>Matrices>Types of Matrices

If

w

is a complex cube root of unity, then the matrix

A = [\begin{array}{l} 1 & ω^{2} & ω \\ ω^{2} & ω & 1 \\ ω & 1 & ω^{2} \end{array}]

is a-

EASY

Mathematics>Algebra>Matrices>Types of Matrices

The number of all possible matrices of order

3 \times 3

with each entry

0

or

1

is

EASY

Mathematics>Algebra>Matrices>Types of Matrices

If

A = [\begin{matrix} 1 & - \tan θ \\ \tan θ & 1 \end{matrix}] & A A^{- 1} = [\begin{matrix} a & - b \\ b & a \end{matrix}]

, then

EASY

Mathematics>Algebra>Matrices>Types of Matrices

A diagonal matrix whose diagonal elements are all equal is called a_____matrix.

EASY

Mathematics>Algebra>Matrices>Types of Matrices

If

A = [\begin{array}{l} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{array}]

then

A^{5} =

EASY

Mathematics>Algebra>Matrices>Types of Matrices

If

A = [\begin{array}{l} 4 & x + 2 \\ 2 x - 3 & x + 1 \end{array}]

is symmetric, then

x =

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Mathematics>Algebra>Matrices>Types of Matrices

Let

A [\begin{array}{l} 1 & 2 \\ 3 & 4 \end{array}]

and

B = [\begin{array}{l} a & b \\ c & d \end{array}]

are two matrices such that

A B = B A

and

c \neq 0

, then value of

\frac{a - d}{3 b - c}

is

EASY

Mathematics>Algebra>Matrices>Types of Matrices

If

D = diag [d_{1}, d_{2}, \dots . . d_{n}]

is a diagonal matrix with

d_{i} \neq 0, i = 1, 2, 3, . . . . . ., n,

then

D^{- 1}

is

EASY

Mathematics>Algebra>Matrices>Types of Matrices

The matrix

P = [\begin{array}{l} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}]

is

EASY

Mathematics>Algebra>Matrices>Types of Matrices

The product of the matrices

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

and

B = [\begin{array}{l} \cos^{2} ϕ & \cos ϕ \sin ϕ \\ \cos ϕ \sin ϕ & \sin^{2} ϕ \end{array}]

is a null matrix

if

θ - ϕ =

EASY

Mathematics>Algebra>Matrices>Types of Matrices

If

A = (\begin{array}{lll} 1 0 0 \\ 0 1 0 \\ 0 0 1 \end{array})

then

A^{3} =

_____.

EASY

Mathematics>Algebra>Matrices>Types of Matrices

If

A

is a skew symmetric matrix and

n

is odd positive integer then

A^{n}

is -

EASY

Mathematics>Algebra>Matrices>Types of Matrices

Which of the given values of

x

and

y

make the following pair of matrices equal?

$[\begin{matrix} 3 x + 7 & 5 \\ y + 1 & 2 - 3 x \end{matrix}] = [\begin{matrix} 0 & y - 2 \\ 8 & 4 \end{matrix}]$ .

EASY

Mathematics>Algebra>Matrices>Types of Matrices

A matrix which is not a square matrix is called a _____matrix.

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Mathematics>Algebra>Matrices>Types of Matrices

(\begin{array}{cc} a & 2 \\ - 3 & 7 \end{array}) = (\begin{array}{ll} - 6 2 \\ - 3 7 \end{array})

if and only if_____.

EASY

Mathematics>Algebra>Matrices>Types of Matrices

If

[\begin{matrix} a + b & 2 \\ 7 & a b \\ - 3 & 4 \end{matrix}] = [\begin{matrix} 6 & 2 \\ 7 & 8 \\ - 3 & 4 \end{matrix}]

, then