find matrix P such that P × [2 6 -1 8] = [ 4 8 ] Also write the order of matrix P
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Step-by-step explanation:
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Answer:
P = [ 20/11 - 4/11 ]
Step-by-step explanation:
Given :- A matrix P such that P × 2 6 = [ 4 8 ]
- 1 8
To Find :- The matrix P and it's order
Solution :-
It is given that P × 2 6 = [ 4 8 ]
- 1 8
Since the result matrix is of order 1 × 2.
Therefore, both the matrix on left side must be of order x × 2.
One of the given matrix is of order 2 × 2.
∴ P must be of order 1 × 2.
Let the matrix P be [ x y ]
Now [x y ] × 2 6 = [ 4 8 ]
- 1 8
⇒ [ 2x - y 6x + 8y ] = [ 4 8 ]
⇒ 2x - y = 4 ----- ( 1 ) and 6x + 8y = 8 ----- ( 2 )
Here we need to multiply equation ( 1 ) by 3
⇒ 6x - 3y = 12 ----- ( 3 ) and 6x + 8y = 8 ----- ( 4 )
Subtracting equation ( 3 ) from ( 4 ), we get
⇒ 6x + 8y - 8 - 6x + 3y + 12 = 0
⇒ 11 y + 4 = 0
⇒ y = -4/11
Putting y = - 4/11 in equation ( 1 ), we get
⇒ 2x = 4 + ( - 4/11 )
⇒ 2x = ( 44 - 4 )/11
⇒ 2x = 40/11
⇒ x = 20/11
∴ x = 20/11 and y = - 4/11
The matrix P will be [ 20/11 - 4/11 ].
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