Find the whole answer of Ax = b, including all steps.

Question

A =

[2 4 64

2 5 76

2 3 52]

b =

[b1

b2

b3]

=

[4

3

5]

Answer 1

Find the whole answer of Ax = b, including all steps.

A =

[2 4 64

2 5 76

2 3 52]

B =

[4

3

5]

Detailed Solution:

Ax = B ==> A^-1Ax = A^-1B ==> Ix = A^-1B ==> x = A^-1B (Final Answer)

As shown above, find the inverse matrix of A which is A^-1; then multiply it by B; the result is x

You can do this manually or in TI-84 Plus:

Create: 3 x 3 Matrix A and 3 x 1 Matrix B, then simple do the following in TI-84 Plus: [A]^-1[B]

This will give you the Final Answer: x =

Note: I tried this and did not work because the inverse of Matrix A does not exist; A is singular Matrix i.e. there is no A^-1. As it is given the answer is: No Solution or You need to double check the numbers in your Matrix A.

To get a valid answer, I have tweaked Matrix A a little bit - changed the last number from 52 to 51; and here is the result of: [A]^-1[B]

x =

[4

-1

0]

Answer 2

You need to find the inverse matrix of A, let's call it A-. Then you multiply [A-][b]