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I have to solve for x, y and z but I'm not sure how. I was told to use this equation so I already made A the inverse, but I'm not sure what to do next...\[A^-1\times B \]
where is your A^-1 matrix? can you draw it on here? It seems that after we find the inverse we're supposed to use matrix multiplication
ok so then we need to use matrix multiplication . your A^-1 matrix is a 3 x 3 matrix and your B is a 3 x 1 matrix so your A^-1 x B should be a 3 x 1 matrix.
I'm not sure how to do that multiplication...
Is this going to solve x y and z?
only because we have an m x n matrix and a n x p matrix . They share the same dimension size in the middle so the end result is m x p 3 x 3 A^-1 3 x 1 B 3 x 3 3 x 1 3 x 1 should be your end result... but I don't think it's going to lead farther enough to solve the equation because after you do matrix multiplication that new matrix will be to be written down x y z = 4 4x 4y 0 z = 3 0x+y-3z = -10 then since you have an augmented matrix of A l B 1 1 1 l 4 4 4 0 l 3 0 1 -3 l -10 then we use row operations.
we need the terms below the main diagonal 0 with row operations that should be easy, but you really need is a reduced row echelon matrix. which means the terms above the diagonal have to go to 0 too... the operations apply to the entire row
whoa I'm lost...
I lost it right after you said 'then since you have an augmented matrix of A l B '
do you know row operations for a matrix? Like how to make it echelon form or reduce row echelon form?
oh you know I found it on a site where it explains it step by step but thank you SO much for helping me
I think you can just take matrix multiplication on the left side of the original matrix and then use row operations... then you will find x y z but the numbers are going to be bigger while you're doing row operations. so when you have a format like 1 0 0 l 3 0 1 0 l 5 0 0 1 l 5 that means x = 3, y =5, and z=5 (just an example) if you plug those values back into the original equation you will know if the entire left matrix = the right matrix a.k.a A =B. I had a hard time with these when I first started but when I practiced and learned the rules, it became easy afterwards.