Find the inverses of the following matrices A and use them t

Find the inverses of the following matrices A and use them to solbe Ax=b

Solution

Given AX = B

we can multiply both sides by the inverse of A, provided this exists, to give A^-1AX = A^-1B

But AA = I, the identity matrix.

Furthermore, IX = X,

because multiplying any matrix by an identity matrix of the appropriate size leaves the matrix unaltered.

So X = A^-1B

if AX = B, then X = A^-1B

here x= [x

y]

so take

Ax=B is A= 1 4 3

1 4 5

2 5 1

b= 6

0

6

here 1 4 3 | x| 6

1 4 5 |y| = 0

2 5 1 | z| 6

by above the equations are like this

x+4y+3z=6

x+4y+5z=0

2x+5y+z=6

then

A= 1 4 3

1 4 5

2 5 1

take the formula like this A^-1= 1/x1y2+x2y1 then you will get

x=Ab then you got what is x=?