Equality of Matrices

Q. Given $\left[\begin{array}{cc}x& y+2\\ 3& z-1\end{array}\right]=\left[\begin{array}{cc}3& 1\\ 3& 2\end{array}\right]$; then find the value of x+y +z.

1. 6
2. 4
3. 5
4. 8

Q.

Find the value of x, given that $A^2$ = B,

A= $\left[\begin{array}{cc}2& 12\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}4& x\\ 0& 1\end{array}\right]$
___

Q.

If $A=\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$ and $A^2$ = I then x = ___

Q.

Solve for x and y:
$\left[\begin{array}{cc}-2& 0\\ 3& 1\end{array}\right]\left[\begin{array}{c}-1\\ 2x\end{array}\right]+3\left[\begin{array}{c}-2\\ 1\end{array}\right]=2\left[\begin{array}{c}y\\ 3\end{array}\right]$

1. -3, -2

2. 3, 2

3. 3, -2

4. -3, 2

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, -4, -9

4. -6, 12, 18

Q.

If $(\begin{array}{cc}{a}^2-b^2& b\\ a& 3\end{array})$ = $(\begin{array}{cc}-x& 5\\ 2& 3\end{array})$, the value of x is ___.

Q.

Consider A = $(\begin{array}{cc}x+y+z& 3\\ 0& 12\end{array})$ = $(\begin{array}{cc}-a& z\\ x+z& -y\end{array})$. The value of a is ___

Q.

Which of the following are equal matrixes.

$A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$
$B=\left[\begin{array}{ccc}1& 2& 4\\ 3& 5& 6\\ 7& 8& 9\end{array}\right]$
$C=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$
$D=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$
$E=\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]$

1. A & B are equal and C & E are equal

2. A &D are equal

3. C & E are equal

4. None of these

Q. Let $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\text{and}B=\left[\begin{array}{cc}a& 0\\ 0& b\end{array}\right],a,b,ϵN.$ Then

1. there cannot exists any B such that AB = BA.
2. there exists more than one but finite number of B's such that AB = BA.
3. there exists exactly one B such that AB = BA.
4. there exists infinitely many B's such that AB = BA.

Q.

If A and B are two matrices such that AB=B and BA=A, then $A^2+B^2$=

1. $2AB$

2. $2BA$

3. $A+B$

4. $AB$