Math, asked by kimtaehyung15, 1 month ago

find matrix P such that P × [2 6 -1 8] = [ 4 8 ] Also write the order of matrix P


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Answers

Answered by singhishita119
0

Step-by-step explanation:

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Answered by vinod04jangid
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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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