Question

Find the matrices X and Y if 2X+Y=[(4, 4,7), (7, 3,4) ]and X-2Y=[(-3, 2,1), (1, -1, 2) ]​

Answer 1

Answer:

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Step-by-step explanation:

here we calculate it by multipying the second eq by 2 then

2x-4y =((-6 4 2 ) ,(2 , -2 4) )

now subract the the both eq then we get the value of y

y = ((2 ,0 , 1) , (1,1,0) )

now put this value in any eq then we get the valu e of x

x = ( (1,2,3 ),(3,1,2)

hope help u

Answer 2

Step-by-step explanation:

Given:

$2X+Y=\left[\begin{array}{ccc}4&4&7\\7&3&4\end{array}\right]...eq1$

$X-2Y=\left[\begin{array}{ccc}-3&2&1\\1&-1&2\end{array}\right]...eq2$

To find: Find the matrix X and Y.

Solution:

Step 1: Multiply eq1 by 2

$4X+2Y=\left[\begin{array}{ccc}8&8&14\\14&6&8\end{array}\right]$

Step 2: Add both equations

$4X+2Y=\left[\begin{array}{ccc}8&8&14\\14&6&8\end{array}\right]$

$X-2Y=\left[\begin{array}{ccc}-3&2&1\\1&-1&2\end{array}\right]$

_____________________________

$5X=\left[\begin{array}{ccc}5&10&15\\15&5&10\end{array}\right]$

_____________________________

Divide by 5

$X=\left[\begin{array}{ccc}1&2&3\\3&1&2\end{array}\right]$

Step 3: Put value of X in eq1

$2\left[\begin{array}{ccc}1&2&3\\3&1&2\end{array}\right]+Y=\left[\begin{array}{ccc}4&4&7\\7&3&4\end{array}\right]$

$\left[\begin{array}{ccc}2&4&6\\6&2&4\end{array}\right]+Y=\left[\begin{array}{ccc}4&4&7\\7&3&4\end{array}\right]$

$Y=\left[\begin{array}{ccc}4&4&7\\7&3&4\end{array}\right]-\left[\begin{array}{ccc}2&4&6\\6&2&4\end{array}\right]$

$Y=\left[\begin{array}{ccc}2&0&1\\1&-1&2\end{array}\right]$

Final answer:

$\bf X=\left[\begin{array}{ccc}1&2&3\\3&1&2\end{array}\right]$

$\bf Y=\left[\begin{array}{ccc}2&0&1\\1&-1&2\end{array}\right]$

Hope it helps you.

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