Matrices and Determinants - Set 1

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Matrices and Determinants - Set 1

MM

Mashaal Masha

Sep 28, 2022

Table of Contents

Choose the correct options for the following questions.

Determinant of $\begin{bmatrix}x& 1& 1 &1 \\1&x & 1 & 1\\1&1&x & 1\\1&1&1&x \end{bmatrix}$=

Difficulty: Easy

A:

0

B:

(x-1)

C:

x+3

D:

(x+3)(x-1)

Find the cofactor of 1 in the matrix $A = \begin{bmatrix}1 & 3 \\2 & 4 \end{bmatrix}$

Difficulty: Easy

A:

$1$

B:

$-1$

C:

$4$

D:

$-4$

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If determinant of $A=\begin{bmatrix}4& 0 &0 \\0&-2& 0 \\0&0&3 \end{bmatrix}$ then $A_{11}$=

Difficulty: Easy

A:

6

B:

8

C:

5

D:

-6

Orders of some matrices are given below. Which one of them cannot be multiplied?

Difficulty: Easy

A:

a x b, b x c where a, b and c are all positive integers

B:

3 x 5, 4 x 1

C:

m x n, n x p where m, n and p are all positive integers

D:

1 x 2, 2 x 4

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Null matrix of order $1\times2$ is

Difficulty: Easy

A:

\begin{bmatrix}0 \\0 \end{bmatrix}

B:

\begin{bmatrix}0 & 0 \end{bmatrix}

C:

\begin{bmatrix}0 & 0 \\ 0 & 0 \end{bmatrix}

D:

None of these

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Null matrix of order $1\times2$ is

Difficulty: Easy

A:

\begin{bmatrix}0 \\0 \end{bmatrix}

B:

\begin{bmatrix}0 & 0 \end{bmatrix}

C:

\begin{bmatrix}0 & 0 \\ 0 & 0 \end{bmatrix}

D:

None of these

Inverse of $A=\begin{bmatrix}1 & 2 \\3 & 4 \end{bmatrix}$ is:

Difficulty: Easy

A:

\begin{bmatrix}1 & -2 \\3 & 0 \end{bmatrix}

B:

\begin{bmatrix}-2 & 1 \\1.5 & -0.5 \end{bmatrix}

C:

\begin{bmatrix}0 & 0 \\0 & 0 \end{bmatrix}

D:

None of the these

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Inverse of $A=\begin{bmatrix}1 & 2 \\3 & 4 \end{bmatrix}$ is:

Difficulty: Easy

A:

\begin{bmatrix}1 & -2 \\3 & 0 \end{bmatrix}

B:

\begin{bmatrix}-2 & 1 \\1.5 & -0.5 \end{bmatrix}

C:

\begin{bmatrix}0 & 0 \\0 & 0 \end{bmatrix}

D:

None of the these

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Inverse of $A=\begin{bmatrix}a & b \\c & d \end{bmatrix}$ is:

Verified

Difficulty: Easy

A:

12

B:

$-42$

C:

21

D:

None of these

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Find the values of $x$ if $\begin{vmatrix}3 & 1 & x \\-1 & 3 & 4 \\ x & 1 & 0 \end{vmatrix}=-30$

Difficulty: Easy

A:

$-2,3$

B:

$3,-4$

C:

$2,-3$

D:

$4,-3$

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