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Perform elementary row operations on A to transform it into B.
The elementary matrices corresponding to each row operation will give us E1, E2, and E3.
Given matrices A and B: A = [1, 2, 3; 1, 4, 1; 2, 1, 9] B = [1, 0, 5; 0, 2, -2; 1, 1, 4]
We need to find elementary matrices E1, E2, and E3 such that E3 * E2 * E1 * A = B.
Performing the row operations to transform A into B, we get:
R3 = R3 - 2*R1
R2 = R2 - R1
R3 = R3 - R2
The corresponding elementary matrices are: E1 = [ 1, 0, 0; -1, 1, 0; 0, 0, 1 ]
E2 = [ 1, 0, 0; 0, 1, 0; 0, -1, 1 ]
E3 = [ 1, 0, 0; 0, 1, 0; -1, 0, 1 ]
Therefore, the elementary matrices E1, E2, and E3 such that CA = B are as follows: E1 = [ 1, 0, 0; -1, 1, 0; 0, 0, 1 ]
