| 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.
2 answers
1kw
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].
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].