Question

what is the solution of the matrix equation?

[ 5 -2] X= [2]
2 -1 -4

Answer 1

So you have any idea how to find the order of matrix X ?

Answer 2

no clue..

Answer 3

Ok at least you know that order of [ 5 -2
2 -1 ] is (2x2)?

Answer 4

yea i do

Answer 5

Yes. so let Order of matrix X be (a x b )

And order of product matrix is (2x1)

We know that matrices can be multiplied if no of columns of 1st matrix equals no. of rows of X.

Then no . of rows of X = 2.

And if (a x b) . ( c x d) matrix is multiplies, result is always matrix of order (a x d)

Hence no. of columns in X = 1. (since product matrix of order (2x1) would be d= 1)

So order of X = ( 2 x 1 ). Ok till here?

Answer 6

ya i got it so far i think

Answer 7

[ 5 -2] ( x y ) = [2]
2 -1 -4

This would mean -

5.x - 2.y => 2

2.x - 1.y -4

(5x - 2y => 2

2x - y) -4.


Now the matrices are equal; hence their corresponding elements are equal as well.

so 5x-2y = 2, 2x-y = -4, ok?

Answer 8

alright ya. so now how do you solve it from here?. it's not like a linear equation is it?

Answer 9

Well nope. these are simultaneous equations.

5x-2y = 2, 2x-y = -4.

You can solve it using substitution method.

2x - y = -4 so y = 2x+4

Use y = 2x + 4 in 5x-2y = 2, u'll get the value of x.

hence solve the value of Y.

The matrix X will be (x y)

Answer 10

oh alright i didnt think it was linear, im just not familiar with matrices

Answer 11

haha no probs..hope u got the right ans :)

Answer 12

me too thanks for the help!