Question

please guys help to do this please​

Answer 1

Answer :-

The values of x and y are 2 and -8.

Step-by-step explanation :-

Given :

If ${2\left[\begin{array}{ccc}3&4\\5&x\end{array}\right]}$ + $\left[\begin{array}{ccc}1&y\\0&1\end{array}\right]$ = $\left[\begin{array}{ccc}2&0\\10&5\end{array}\right]$.

To find :

Values of x and y ?

Solution :

${2\left[\begin{array}{ccc}3&4\\5&x\end{array}\right]}$ + $\left[\begin{array}{ccc}1&y\\0&1\end{array}\right]$ = $\left[\begin{array}{ccc}2&0\\10&5\end{array}\right]$

$\left[\begin{array}{ccc}6&8\\10&2x\end{array}\right]$ + $\left[\begin{array}{ccc}1&y&\\0&1\end{array}\right]$ = $\left[\begin{array}{ccc}2&0\\10&5\end{array}\right]$

$\left[\begin{array}{ccc}6+1&8+y\\10+0&2x+1\end{array}\right]$ = $\left[\begin{array}{ccc}2&0\\10&5\end{array}\right]$

Now,

[8 + y] = 0

[2x + 1] = 5

We get,

8 + y = 0

y = 0 - 8

∴ y = -8

2x + 1 = 5

2x = 4

∴ x = 2

∴ The values of x and y are 2 and -8.

Answer 2

Answer:

x = 2

y = - 8

Step-by-step explanation:

Correct question :-

$If\: 2\begin{bmatrix}3&4\\5& x\end{bmatrix}+\begin{bmatrix}1& y\\0& 1\end{bmatrix}=\begin{bmatrix}7& 0\\10& 5\end{bmatrix}$

Find the values of x , y .

Given ,

$2\begin{bmatrix}3&4\\5& x\end{bmatrix}+\begin{bmatrix}1& y\\0& 1\end{bmatrix}=\begin{bmatrix}7& 0\\10& 5\end{bmatrix}$

To Find :-

Values of x , y .

Formula Required :-

$x\begin{bmatrix}a&b\\c&d\end{bmatrix}=\begin{bmatrix}x\times a&x\times b\\x\times c&x\times d\end{bmatrix}$

$\begin{bmatrix}a&b\\c&d\end{bmatrix}+\begin{bmatrix}p&q\\r&s\end{bmatrix}=\begin{bmatrix}a+p&b+q\\c+r&d+s\end{bmatrix}$

Solution :-

$2\begin{bmatrix}3&4\\5& x\end{bmatrix}+\begin{bmatrix}1& y\\0& 1\end{bmatrix}=\begin{bmatrix}7& 0\\10& 5\end{bmatrix}$

$\begin{bmatrix}2\times 3& 2\times 4\\2\times 5& 2\times x\end{bmatrix}+\begin{bmatrix}1& y\\0& 1\end{bmatrix}=\begin{bmatrix}7& 0\\10& 5\end{bmatrix}$

$\begin{bmatrix}6& 8\\10& 2x\end{bmatrix}+\begin{bmatrix}1& y\\0& 1\end{bmatrix}=\begin{bmatrix}7& 0\\10& 5\end{bmatrix}$

$\begin{bmatrix}6+1& 8+y\\10+0& 2x+1\end{bmatrix}=\begin{bmatrix}7& 0\\10& 5\end{bmatrix}$

$\begin{bmatrix}7& 8+y\\10& 2x+1\end{bmatrix}=\begin{bmatrix}7& 0\\10& 5\end{bmatrix}$

By comparing both matrices :-

8 + y = 0 , 2x + 1 = 5

First equating '8 + y = 0' :-

8 + y = 0

y = - 8

∴ Value of 'y' = - 8

Equating '2x + 1 = 5' :-

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

∴ Value of 'x' =  2

∴ x , y = 2 , - 8