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Equation in Matrix

I have problem in center of Terwilliger Algebra. But, I will explain simple problem for simplicity my problem.

For example, I have matrix


and also I have


These matrix have condition


for any B=B1,B2,B3,B4 If I solve it by hand, it is easy to get a1,a2,a3,a4. But how to do it by sage? Can sage solve it? Thanks