Let W = Span{A1,A2,A3,A4}, where A1 = [4 1;2 1], A2 = [1 1;2 1], A3 = [0 2; 1 1]

Question

Let W = Span{A1,A2,A3,A4}, where A1 = [4 1;2 1], A2 = [1 1;2 1], A3 = [0 2; 1 1], A4 = [2 1; -1 0]     (matrix are all 2 x 2)

a) Find basis for W

b) is the matrix H = [-1 3; 3 1] (also 2 x 2) an element of W?

For part 1.

I just wrote the Ai matrices as columns and found the linear independent rows.. however, when explaining which are the basis, do I just state the matrices that are linearly independent?

For part 2. I know I have to write H as a linear combination of the span. But, do I just use the linear independent rows to do it?


PLEASE explain how I would go about solving.. I will gladly give full points.. thank you!

Explanation / Answer

For part 1:The basis of W consists of only the liner independent row.So, when explaining which are the basis, you just have to state the matrices that are linearly independent

For part 2:Here again, only the linear independent rows must be used to express H as a linear combination of these linear independent rows.

Hope this helps.Let me know if you have further doubts

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