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Question 174917: i have the following 3x3 matrix
1,2,-1
2,1,4 = A
1,-2,1
i need to evaluate A^2 and A^3 but i cant even figure out where to start, any help would be greatly appreciated
Answer by actuary(112)   (Show Source):
You can put this solution on YOUR website! The problem asks you to multiply matrices. A^2 =A*A and A^3=A*A*A
1,2,-1
A = 2,1,4
1,-2,1
The first row, first column of A*A = A^2 is calculated by multiplying each element of the first row of A by each element of the first column of A and then each of the products are added together.
The second row, first column of A*A = A^2 is calculated by each element of the second row of A by each element of the first column of A and then each of the products are added together.
The third row, first column element of A*A = A^2 is calculated by each element of the third row of A by each element of the first column of A and then each of the products are added together.
The general rule that is being used is the i'th row and j'th column element of the result is found by multiplying each element in the i'th row of one matrix(multiplier) by each element of the j'th column of the other matrix (multiplican) and then the products are added to together.
So to calculate A^2 you have to calculate 9 numbers using the rule that is described above.
Since A^3 = (A^2)*A, you have to calculate 9 numbers using the rule described above with A^2 being one matrix and A the other matrix.
I hope that this helps but it does take some practice to understand and be able to do matrix multiplication.
Good luck.
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