# Algebra

posted by .

| 2 3 5|
A=| 1 7 9|
|-3 2 10|

,

|3|
B=|4|
|1|

I need to solve this matrix equation
AX = B FOR X BY FINDING A^-1, given A and B as follows. I am new at this did I write A^1 right? This is suppose to be an A with a minus one at the top.

• Algebra -

1kw

• Algebra -

Given A and B, where A is a 3x3 matrix, and B is a vector of 3, and

AX=B

To solve for X, we would pre-multiply by the inverse of A to give
A-1A X = A-1B
Since A-1A is the identity matrix by definition of the inverse, we end up with
X = A-1B

To find X, it will be necessary to find the inverse of A, premultiply with B and the result (3x1 vector) will be X as required.

The inverse of A can be found by Gauss elimination, or any other method that you have learned.

The value of X is a multiple or sub-multiple of [17,4,7].

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