Scalar Multiplication of a Matrix

Q.

Which of the following is correct about scalar multiplication of a matrix A?

1. Every element of a particular row is multiplied by the scalar when a matrix is multiplied by the scalar.

2. Every element of the matrix is multiplied with the scalar when a matrix is multiplied with a scalar.

3. One of the elements of the matrix is multiplied with the scalar when a matrix is multiplied with the scalar.

4. Every element of a particular column is multiplied by the scalar when a matrix is multiplied by the scalar.

Q.

If $M=\left[\begin{array}{c}0\\ 1\end{array}\right]$ and $N=\left[\begin{array}{c}1\\ 0\end{array}\right]$

Show that $3M+5N=\left[\begin{array}{c}5\\ 3\end{array}\right]$

Q.

If the number of rows and columns of a matrix are not equal, then the matrix is called __ matrix.

Q. Which of the following represents the column matrix for the above graphical representation?

1. $\left[\begin{array}{c}-2\\ 3\end{array}\right]=\left[\begin{array}{c}x\\ y\end{array}\right]$
2. $\left[\begin{array}{c}2\\ -3\end{array}\right]=\left[\begin{array}{c}x\\ y\end{array}\right]$
3. $\left[\begin{array}{c}3\\ -2\end{array}\right]=\left[\begin{array}{c}x\\ y\end{array}\right]$
4. $\left[\begin{array}{c}2\\ -3\end{array}\right]=\left[\begin{array}{c}y\\ x\end{array}\right]$

Q.

Find a and b if
$a\left[\begin{array}{c}1\\ 7\end{array}\right]-\left[\begin{array}{c}3\\ b\end{array}\right]=\left[\begin{array}{c}2\\ 24\end{array}\right]$

1. a= -11, b = -5
   

2. a= -5, b = -11
   

3. a= 11, b = 5

4. a= 5, b = 11

Q.

If $H=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 3& 1& 2\end{array}\right]G=\left[\begin{array}{ccc}2& 6& -10\\ 0& -4& 8\\ 2& -8& 4\end{array}\right]$

Find $3H-\frac{1}{2}G$

1. $\left[\begin{array}{ccc}2& 3& 14\\ 6& 11& -1\\ 8& 7& 4\end{array}\right]$

2. $\left[\begin{array}{ccc}2& 3& 14\\ 1& 0& 1\\ 8& 7& 4\end{array}\right]$

3. $\left[\begin{array}{ccc}-2& 8& 2\\ 6& 11& -1\\ 8& 7& 4\end{array}\right]$

4. $\left[\begin{array}{ccc}2& 3& 14\\ 6& 11& -1\\ 3& 0& -2\end{array}\right]$

Q. $\text{Let}A=\left[\begin{array}{ccc}-8& 3& 1\\ 4& 7& 2\end{array}\right]\text{What is the order of matrix A?}$

[1 mark]

1. $3\times 2$
   
2. $3\times 3$
3. $2\times 3$
4. $3\times 1$

Q.

If $A=\left[\begin{array}{cc}1& 2\\ -3& 1\end{array}\right]\text{and}B=\left[\begin{array}{cc}11& -1\\ 4& 3\end{array}\right]$

Find Matrix X, given that
X-5A=3B

1. $\left[\begin{array}{cc}38& -7\\ 3& 14\end{array}\right]$

2. $\left[\begin{array}{cc}8& 7\\ 3& 14\end{array}\right]$

3. $\left[\begin{array}{cc}8& 7\\ -3& -4\end{array}\right]$

4. $\left[\begin{array}{cc}38& 7\\ -3& 14\end{array}\right]$

Q.

Evaluate $3\left[\begin{array}{cc}1& -1\\ -2& 0\\ 1& -2\end{array}\right]-\left[\begin{array}{cc}-5& 2\\ -1& 3\\ 4& -4\end{array}\right]$

1. $\left[\begin{array}{cc}8& 5\\ 5& 3\\ 1& 2\end{array}\right]$

2. $\left[\begin{array}{cc}8& -5\\ -5& -3\\ -1& -2\end{array}\right]$

3. $\left[\begin{array}{cc}8& -5\\ 7& 4\\ 1& 2\end{array}\right]$

4. $\left[\begin{array}{cc}2& 1\\ 5& 3\\ -1& -2\end{array}\right]$

Q.

If$A=\left[\begin{array}{cc}1& 2\\ -2& 9\end{array}\right]$, then -2A=_______________

1. 

2. 

3. 

4. 

Q.

If $A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$, $kA=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]$, then the values of k, a, b respectively are ______ .

1. -6, -12, -16

2. -6, 4, -9

3. -6, 12, 18

4. -6, -4, -9

Q.

If $H=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 3& 1& 2\end{array}\right]G=\left[\begin{array}{ccc}2& 6& -10\\ 0& -4& 8\\ 2& -8& 4\end{array}\right]$

Find $3H-\frac{1}{2}G$

Q. If $A=\left[\begin{array}{cc}0& 2\\ 3& -4\end{array}\right]$ and $kA=\left[\begin{array}{cc}0& 3a\\ 2b& 24\end{array}\right]$, then the values of k, a, b are respectively.

1. -6, 4, 9
2. -6, -4, -9
3. -6, 12, 18
4. -6, -12, -18

Q.

If $A=\left[\begin{array}{cc}1& 1\\ 2& 33\end{array}\right]$and 2A – B =0, find B.

Q. $\text{If}\left[\begin{array}{cc}x+2& 0\\ 3& y-1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 3& 1\end{array}\right],$
$\text{then the value of}(x+y)\text{is equal to :}$


[1 Marks]

1. 0
2. 1
3. 2
4. 3

Q.

If A = $\left[\begin{array}{ccc}1& 4& 5\\ 3& 2& 6\end{array}\right]$ then second element of second row of 3A =

___

Q. Let $g\left(x\right)=\left|\begin{array}{ccc}f(x+c)& f(x+2c)& f(x+3c)\\ f\left(c\right)& f\left(2c\right)& f\left(3c\right)\\ f^{\prime }\left(c\right)& f^{\prime }\left(2c\right)& f^{\prime }\left(3c\right)\end{array}\right|$, where $c$ is constant then $\underset{x\to 0}{lim}\frac{g\left(x\right)}{x}$ is equal to

1. $0$
2. $1$
3. $-1$
4. $f\left(c\right)$

Q.

If$A=\left[\begin{array}{cc}1& 2\\ -2& 9\end{array}\right]$, then -2A=_______________

1. 

2. 

3. 

4. 

Q. When a scalar is multiplied to a matrix, the number of rows in the matrix

1. gets doubled
2. remains same
3. gets tripled
4. becomes zero

Q.

If $H=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 1\\ 3& 1& 2\end{array}\right]G=\left[\begin{array}{ccc}2& 6& -10\\ 0& -4& 8\\ 2& -8& 4\end{array}\right]$

Find $3H-\frac{1}{2}G$ [3 Marks]

Q. When a scalar is multiplied to a matrix, the number of rows in the matrix

1. gets doubled
2. gets tripled
3. remains same
4. becomes zero

Q. Scalar multiplication involves the multiplication of whole matrix by a variable.

1. False
2. True