In Exercises 5-8, for the matrices A(2*2) =[2 4 3 1]andB(2*2) =[0 1 5 2] in M2,2, determine whether the given matrix is a linear combination of A and B.

[0 0] = a[2 4 ] + b[0 1 ]

[0 0] [3 1] [5 2]

I know that a and b are 0 but why this matrix is not a linear combination of A and B?

I think 0 = 0 v₁ + 0v₂

can be a linear combination of A and B.

Can you explain it?

thank you