Multiplication of Matrices

Q.

$Howdoyoumultiply2x3and2x2matrices?$

Q.

$Adj(AdjA)$ is equal to ___, if $A$ is a square matrix of order $n$.

1. $|A{|}^{n-1}A$

2. $|A{|}^{n}A$

3. $|A{|}^{n-2}A$

4. None of these

Q.

If $\left[\begin{array}{cc}a+b& 2\\ 5& ab\end{array}\right]=\left[\begin{array}{cc}6& 2\\ 5& 8\end{array}\right]$ , find the values of a and b.

Q.

What is truth table and its significance?

Q.

If $A=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$, then $A^4$=__________________

1. 

2. 

3. 

4. 

Q.

The minimum value of $\left|a+b\omega +c{\omega }^2\right|$, where $a,b$and $c$ are all not equal integers and omega ( not equal $1$)is a cube root of unity, is

1. $\sqrt{3}$

2. $\frac{1}{2}$

3. $1$

4. $0$

Q.

Express $64$ as the sum of $8$ odd numbers.

Q.

Solve the equation by factorization: $x^2-10x+21=0$.

Q.

Can a determinant be negative?

Q.

Matrix A has x rows and x + 5 columns. Matrix B has y rows and 11 - y columns. Both AB and BA exist.Then, the value of x and y is

1. 3, 9

2. 8, 3

3. 3, 8

4. 4, 8

Q.

The order of the matrix A is 3 $\times$ 5 and that of B is 2 $\times$ 3. The order of the matrix BA is

1. 3 × 2

2. 2 × 5

3. 2 × 3

4. 5 × 2

Q. If A and B are two square matrices of order 3 $\times$ 3 which satisfy AB = A and BA = B then $(A+B{)}^7$ is

1. $7.I_{3\times 3}$
2. $64(A+B)$
3. $7(A+B)$
4. $128I_{3\times 3}$

Q.

Order of matrix A is 3 $\times$ 5 and that of B is 2 $\times$ 3. Then then order of the matrix BA is

1. 3 × 2

2. 2 × 3

3. 2 × 5

4. 5 × 2

Q. Let A and B be square matrices of same order satisfying AB = A and BA = B. Then $A^2{B}^2$ equals, (O being the zero matrix of the same order as B)

1. A
2. B
3. I
4. O

Q.

If [1 2 3] A = [4 5], the order of matrix A is

1. 3 x 2

2. 3 x 1

3. 2 x 3

4. 2 x 1

Q.

Evaluate ; if possible:
$\left(i\right)\left[\begin{array}{cc}3& 2\end{array}\right]\left[\begin{array}{c}2\\ 0\end{array}\right]\left(ii\right)\left[\begin{array}{cc}1& -2\end{array}\right]\left[\begin{array}{cc}-2& 3\\ -1& 4\end{array}\right]\left(iii\right)\left[\begin{array}{cc}6& 4\\ 3& -1\end{array}\right]\left[\begin{array}{c}-1\\ 3\end{array}\right]\left(iv\right)\left[\begin{array}{cc}6& 4\\ 3& -1\end{array}\right]\left[\begin{array}{cc}-1& 3\end{array}\right]$
IF not possible Give a reason.

Q.

if X sin^3A + Y cos^3A = (sinA)(cosA) and X sinA = Y cosA , prove that X^2 + Y^2 = 1

Q. Choose the correct option and justify your choice:
$\frac{2\tan {30}^{\circ }}{1+{\tan }^2{30}^{\circ }}=$

1. $\sin {60}^{\circ }$
2. $\cos {60}^{\circ }$
3. $\tan {60}^{\circ }$
4. $\sin {30}^{\circ }$

Q.

Given A$=\left[\begin{array}{ccc}0& 4& 6\\ 3& 0& -1\end{array}\right]$
$B=\left[\begin{array}{cc}0& 1\\ -1& 2\\ -5& -6\end{array}\right]$
is the following possible:
(i) AB (ii) BA (iii) $A^2$

Q. If $A=\left[\begin{array}{cc}2& 5\\ 1& 3\end{array}\right],B=\left[\begin{array}{cc}4& -2\\ -1& 3\end{array}\right]$ and $I$ is Identity matrix of same order and $A^t$ is the transpose of matrix $A$ find $A^t.B+BI$

Q.

Find.$3-3\times 0+\frac{3}{3}=?$

Q.

What is matrix multiplication used for?

Q.

If A and B are square matrices of the same order and AB = BA = A, then B is called ________ matrix.

1. unit

2. Scalar

3. diagonal

4. row

Q. If A and B are two square matrices of order 3 $\times$ 3 which satisfy AB = A and BA = B then $(A+B{)}^7$ is

1. ${7.1}_{3\times 3}$
2. ${1281}_{3\times 3}$
3. $7(A+B)$
4. $64(A+B)$

Q. 50 If xcosB - cosA =0 and ysinB -cosA= 0 then the value of cos square A will be?

Q.

Find a, b, c and d, if $3\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]=\left[\begin{array}{cc}a& 6\\ -1& 2d\end{array}\right]+\left[\begin{array}{cc}4& a+b\\ c+d& 3\end{array}\right]$

Q.

If $A=\left[\begin{array}{ccc}0& 1& 2\\ 1& 2& 3\\ 2& 3& 4\end{array}\right]$ and $B=\left[\begin{array}{cc}1& -2\\ -1& 0\\ 2& -1\end{array}\right]$, then what would be third element in the second column of matrix AB?

1. -8

2. -5
3. 5
4. 7

Q. $\frac{2x}{a}+\frac{y}{b}=2,\frac{x}{a}-\frac{y}{b}=4$

1. $\frac{2}{a},\frac{2}{b}$
2. $2a,-2b$
3. $-2a,2b$
4. $\frac{a}{2},-\frac{b}{2}$

Q. Choose the correct option. Justify your choice.
$\frac{1+{\tan }^{2}A}{1+{\cot }^{2}A}=$

1. ${\sec }^{2}A$
2. $-1$
3. ${\cot }^{2}A$
4. ${\tan }^{2}A$

Q.

If A and B are square matrices of the same order and AB = BA = A, then B is called ________ matrix.

1. Scalar

2. diagonal

3. row

4. unit