NCERT Solutions

$\mathrm{A}=\left[a_{i j}\right]_{m \times n}$ is a square matrix, if

(A) $mn$

(C) $m=n$

(D) None of these

Which of the given values of $x$ and $y$ make the following pair of matrices equal

(A) $x=\frac{-1}{3}, y=7$

(B) Not possible to find

(C) $y=7, x=\frac{-2}{3}$

(D) $x=\frac{-1}{3}, y=\frac{-2}{3}$

The number of all possible matrices of order $3 \times 3$ with each entry 0 or 1 is:

(A) 27

(B) 18

(C) 81

(D) 512

A trust fund has ₹ 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide ₹ 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:

Assume X, Y, Z, W and P are matrices of order $2 \times n, 3 \times k, 2 \times p, n \times 3$ and $p \times k$, respectively. Choose the correct answer in Exercises 21 and 22.

(A) $k=3, p=n$

(B) $k$ is arbitrary, $p=2$

(C) $p$ is arbitrary, $k=3$

(D) $k=2, p=3$

If $n=p$, then the order of the matrix $7 \mathrm{X}-5 \mathrm{Z}$ is:

(A) $p \times 2$

(B) $2 \times n$

(C) $n \times 3$

(D) $p \times n$

Choose the correct answer in the Exercises 11 and 12.

(A) Skew symmetric matrix

(B) Symmetric matrix

(C) Zero matrix

(D) Identity matrix

If $\mathrm{A}=\left[\begin{array}{cc} \cos \alpha & -\sin \alpha \ \sin \alpha & \cos \alpha \end{array}\right]$, and $\mathrm{A}+\mathrm{A}'=\mathrm{I}$, then the value of $\alpha$ is

(A) $\frac{\pi}{6}$

(B) $\frac{\pi}{3}$

(C) $\pi$

(D) $\frac{3\pi}{2}$

Matrices A and B will be inverse of each other only if

(A) $\mathrm{AB}=\mathrm{BA}$

(B) $\mathrm{AB}=\mathrm{BA}=0$

(C) $\mathrm{AB}=0, \mathrm{BA}=\mathrm{I}$

(D) $\mathrm{AB}=\mathrm{BA}=\mathrm{I}$

A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below:

Market | Products

--- | ---

I | 10,000 | 2,000 | 18,000

II | 6,000 | 20,000 | 8,000

If $\mathrm{A}=\left[\begin{array}{cc} \alpha & \beta \ \gamma & -\alpha \end{array}\right]$ is such that $\mathrm{A}^{2}=\mathrm{I}$, then

(A) $1+\alpha^{2}+\beta \gamma=0$

(B) $1-\alpha^{2}+\beta \gamma=0$

(C) $1-\alpha^{2}-\beta \gamma=0$

(D) $1+\alpha^{2}-\beta \gamma=0$

If the matrix A is both symmetric and skew symmetric, then

(A) A is a diagonal matrix

(B) A is a zero matrix

(C) A is a square matrix

(D) None of these

If A is square matrix such that $\mathrm{A}^{2}=\mathrm{A}$, then $(\mathrm{I}+\mathrm{A})^{3}-7 \mathrm{A}$ is equal to

(A) A

(B) I - A

(C) I

(D) 3 A