Need some help transition matrix. Already transposed A and B and multiplied them

Question

Need some help transition matrix. Already transposed A and B and multiplied them together, got the wrong answer. Please help :(

Let alpha = {alpha1, alpha2, alpha3, alpha4}, beta = {beta1, beta2, beta3, beta4} and gamma = {gamma1, gamma2, gamma3, gamma4} be a bases of a vector space V. Suppose we have beta1 = 5alpha1 beta2 = 6alpha1 + 7alpha2 beta3 = 10alpha1 + 5alpha2 + 2alpha3 beta4 = 3alpha1 + 3alpha2 + 10alpha3 + 5alpha4 and gamma1 = 5beta4 gamma2 = 4beta3 + 7beta4 gamma3 = 6beta2 + 3beta3 + 6beta4 gamma4 = 6beta1 + 9beta2 + 4beta3 + 6beta4 Find the transistion matrix from the basis alpha to the basis gamma The transition matrix from the basis alpha to the basis gamma is

Explanation / Answer

matrix = [0 0 0 5, 0 0 4 7, 0 6 3 6, 6 9 4 6] * [5 0 0 0 0, 6 7 0 0, 10 5 2 0, 3 3 10 5]

this will give the answer

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