Addition and Subtraction of a Matrix

Q.

If $a$ and $b$ are two vectors such that$\left|a+b\right|=\sqrt{29}$ and$a\times (2i+3j+4k)=(2i+3j+4k)\times b$, a possible value of $(a+b).(-7i+2j+3k)$ is

1. $0$

2. $3$

3. $4$

4. $8$

Q.

Find the value of a and b so that x^{​​​​​​4}+ x^{​​​​​​3}+ 8x²+ax+ b is divisible by . x^{​​​​​​2}+1.

Q.

Given A = [ 2 -3], B = [ 0 2] and C = [-1 4] ; find the matrix X in each of the follwing
(i) X + B = C - A
(ii)A - X = B + C

Q.

Find the additive inverse of the matrix$\left[\begin{array}{ccc}2& 0& -1\\ -2& 34& -13\\ 45& 12& 78\end{array}\right]$

Q.

Define scalar matrix. Give an example.

Q.

If $\left[\begin{array}{cc}1& 4\\ -2& 3\end{array}\right]+2M=3\left[\begin{array}{cc}3& 2\\ 0& -3\end{array}\right]$
Find the matrix M.

Q.

Find the L.C.M. of $a^{2}bc,$ $a{b}^{2}c$ and $ab{c}^2$

1. $a^{2}bc$

2. $c^2{b}^2{a}^2$

3. $ab{c}^2$

4. $a^2{b}^2{c}^2$

Q. a and b are two positive integers such that a+b=a/b+b/a find the value of a^2+b^2

Q.

Given $A=\left[\begin{array}{cc}2& -6\\ 2& 0\end{array}\right],B=\left[\begin{array}{cc}-3& 2\\ 4& 0\end{array}\right]andC=\left[\begin{array}{cc}4& 0\\ 0& 2\end{array}\right]$ Find the matrix X such that
A + 2X = 2B + C.

Q.

$\frac{1}{3!}+\frac{2}{5!}+\frac{3}{7!}+....$is equal to

1. $e$

2. $\frac{e^{-1}}{2}$

3. $\frac{e}{4}$

4. $\frac{e}{6}$

Q.

State, with reason, whether the following are true or false. A, B and C are matrices of order
$2\times 2.$
(i) A + B = B + A
(ii) A - B = B - A
(iii) (B. C ) . A = B. (C . A)
(iv) ( A + B ) . C = A . C + B . C
(v) A. (B -C ) = A. B - A . C
(vi) (A - B ) . C = A. C - B . C
(vii) $A^2-B^2=(A+B)(A-B)$
(viii) $(A-B{)}^2=A^2-2A.B+B^2$

Q. Two matrices can only be added if their are same.

1. Orders
2. Elements
3. heights

Q.

Wherever possible, write each of the following as a single matrix

$\left(i\right)\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]+\left[\begin{array}{cc}-1& -2\\ 1& -7\end{array}\right]$
$\left(ii\right)\left[\begin{array}{ccc}2& 3& 4\\ 4& 6& 7\end{array}\right]-\left[\begin{array}{ccc}0& 2& 3\\ 6& -1& 0\end{array}\right]$
$\left(iii\right)\left[\begin{array}{ccc}0& 1& 2\\ 4& 6& 7\end{array}\right]+\left[\begin{array}{cc}3& 4\\ 6& 8\end{array}\right]$

Q. Which of the following statements is false given AB = A and BA = B where A and B are two $3\times 3$ matrices?

1. $A^{2}B=A^2$
   
2. $ABA=A$
   
3. $BAB=B$
   
4. $A=B$

Q.

If $A=\left[\begin{array}{cc}5& 4\\ 3& -1\end{array}\right],B=\left[\begin{array}{cc}2& 1\\ 0& 4\end{array}\right]$ and $C=\left[\begin{array}{cc}-3& 2\\ 1& 0\end{array}\right]$ then find A + B - C

1. $\left[\begin{array}{cc}10& -3\\ -2& 3\end{array}\right]$

2. $\left[\begin{array}{cc}10& 3\\ 2& 3\end{array}\right]$

3. $\left[\begin{array}{cc}-10& -3\\ -2& -3\end{array}\right]$

4. $\left[\begin{array}{cc}-10& 3\\ 2& -3\end{array}\right]$

Q.

Find a matrix X such that A-X=B, given

$A=\left(\begin{array}{ccc}3& 7& 2\\ -4& -3& 0\\ 5& 1& -2\end{array}\right)andB=\left(\begin{array}{ccc}8& -6& 1\\ 2& 0& -3\\ 3& 4& -1\end{array}\right)$

1. $\left(\begin{array}{ccc}-5& 13& 1\\ 7& 3& 3\\ 2& 3& -1\end{array}\right)$

2. $\left(\begin{array}{ccc}5& 1& 1\\ -7& 3& 3\\ 2& -3& 1\end{array}\right)$

3. $\left(\begin{array}{ccc}5& 1& 1\\ 7& -3& 3\\ 2& -3& -1\end{array}\right)$

4. $\left(\begin{array}{ccc}-5& 13& 1\\ -7& -3& 3\\ 2& -3& -1\end{array}\right)$

Q. If a+1/b+1/c+1/d = 42/29 then find the value of a+b+c-d ?

Q. If $A=\left[\begin{array}{cc}5& 4\\ 3& -1\end{array}\right],B=\left[\begin{array}{cc}2& 1\\ 0& 4\end{array}\right]$ and $C=\left[\begin{array}{cc}-3& 2\\ 1& 0\end{array}\right]$ then find A + B - C

1. $\left[\begin{array}{cc}10& -3\\ -2& 3\end{array}\right]$
2. $\left[\begin{array}{cc}-10& 3\\ 2& -3\end{array}\right]$
3. $\left[\begin{array}{cc}-10& -3\\ -2& -3\end{array}\right]$
4. $\left[\begin{array}{cc}10& 3\\ 2& 3\end{array}\right]$

Q.

If $A=⟮\begin{array}{cc}2& 3\\ -9& 5\end{array}⟯-⟮\begin{array}{cc}1& 5\\ 7& -1\end{array}⟯$ , then find the additive inverse of $A$

1. 

2. 

3. 

4. 

Q.

tinu wrote the answer of (x+8) divided by 8 as (x+1) and mary wrote it as x tinu found that both were wrong how justify your answer

Q. Let A = $\left[\begin{array}{cc}1& 6\\ 2& 5\end{array}\right]$, B = $\left[\begin{array}{cc}3& 4\\ 4& 9\end{array}\right]$ then find sum of diagonal elements of A + B.

1. 18

Q.

Let $A=\left[\begin{array}{ccc}4& 6& -1\\ 3& 0& 2\\ 1& -2& 5\end{array}\right],B=\left[\begin{array}{cc}2& 4\\ 0& 1\\ -1& 2\end{array}\right]$ and C = [3 1 2]. The expression which is not defined is

1. B'B

2. CAB

3. A+B'

4. $A^2+A$

Q.

Add: $3\mathrm{x}+2\mathrm{y}-5\mathrm{z},7\mathrm{x}-3\mathrm{y}+6\mathrm{z},-6\mathrm{x}+2\mathrm{z}$ using the horizontal method.

Q.

Sir

I am Shaun job of class 10, I have a doubt regarding mathematics on the topic of real numbers,

This is the question Sir

Prove that 5⁹⁹+11⁹⁹+17⁹⁹ is always divisible by 33

Thank you for your valuable time Sir

Sincerely

Shaun

Q. If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

1. $X=\left(\frac{1}{7}\right),Y=\left(\frac{2}{7}\right)$
2. $X=\left(\frac{2}{7}\right)I,Y=\left(\frac{1}{7}\right)I$
3. $X=\left(\frac{2}{7}\right),Y=\left(\frac{1}{7}\right)$
4. $X=\left(\frac{1}{7}\right)I,Y=\left(\frac{2}{7}\right)I$

Q.

If $3A+\left[\begin{array}{cc}4& -1\\ -27& 6\end{array}\right]=\left[\begin{array}{cc}2& 0\\ 2& 32\end{array}\right]$ then find A.

Q. $x-y=\frac{x+y}{7}=\frac{xy}{4}$ than xy=?

Q.

Let $A=\left[\begin{array}{cc}2& 1\\ 0& -2\end{array}\right],B=\left[\begin{array}{cc}4& 1\\ -3& -2\end{array}\right]$ and $C=\left[\begin{array}{cc}-3& 2\\ -1& 4\end{array}\right]$ Find: $A^2+AC-5B$

1. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

2. $\left[\begin{array}{cc}23& 3\\ 17& 6\end{array}\right]$

3. $\left[\begin{array}{cc}-23& 3\\ 17& -6\end{array}\right]$

4. $\left[\begin{array}{cc}-23& 3\\ 17& 6\end{array}\right]$

Q.

If A = $\left[\begin{array}{ccc}2& 4& 8\\ 6& 9& 1\\ 8& 7& 5\end{array}\right]$ and B = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ then find the third element of the first row of A - B.

1. 5

Q. If $A=⟮\begin{array}{cc}2& 3\\ -9& 5\end{array}⟯-⟮\begin{array}{cc}1& 5\\ 7& -1\end{array}⟯$ , then find the additive inverse of $A$.