Question

Find matrix P such that Px[2 6
-1. -8]=[-4 8].
Also write the order of
matrix P.​

Answer 1

The required matrix P =  [x  y] = [-4  -4] and its order is 1x2.

Given:

P x $\left[\begin{array}{cc}2&6\\-1&-8\end{array}\right]$ = [-4  8]

To Find:

The matrix P.

Solution:

We need to solve for the matrix P:

P x $\left[\begin{array}{cc}2&6\\-1&-8\end{array}\right]$ = [-4  8]          ....................................(I)

We know that multiplication matrices A, B, and X are feasible only if their orders satisfy the below condition:

$P_{(m * n )}A_{(n*q)} = B_{(m*q)}$

Comparing the above equation to (I), we have:

n = 2

q = 2

m = 1

Hence, matrix P is of order 1x2.

Let P = [x  y]. Hence, equation (I) becomes

[x  y] x $\left[\begin{array}{cc}2&6\\-1&-8\end{array}\right]$ = [-4  8]

⇒ 2x - y = -4 ............................(II)

and 6x - 8y = 8 ............................(III)

On multiplying equation (II) by 3 and subtracting it from equation (III), we have

6x - 8y - 3(2x - y) = 8 - 3(-4)

⇒ 6x - 8y - 6x + 3y = 8 + 12

⇒ -5y = 20

⇒ y = -4

On substituting the above value in equation (II), we have:

2x - (-4) = -4

⇒ 2x = -8

⇒ x = -4

∴ P =  [x  y] = [-4  -4]

Hence the required matrix P = [-4  -4] and its order is 1x2.

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