[1,2] and v [-1,4] in R? belongs to Span(u,v). ) Let u 3 [-1,2] be vectors...

 

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[1,2] and v [-1,4] in R? belongs to Span(u,v). а) Let u 3 [-1,2] be vectors in R2. Show that the vector w = b) Consider the vectors u = [1,2,3], v = [2,3,1], w = [1,1,2]. Show that u, v and w are linearly independent. c) Let a= (: :) - -(; ) and B = C d h be 2 x 2 matrices and let A be a scalar. Prove that (AA + B)" AAT + BT. d) Let A1,..., An be m x mn matrices. Suppose also that B and C are m x m matrices. Given that B E Span(A1,..., An) and B+C E Span(A1,..., An), show that C E Span(A1,..., An). [1,2] and v [-1,4] in R? belongs to Span(u,v). а) Let u 3 [-1,2] be vectors in R2. Show that the vector w = b) Consider the vectors u = [1,2,3], v = [2,3,1], w = [1,1,2]. Show that u, v and w are linearly independent. c) Let a= (: :) - -(; ) and B = C d h be 2 x 2 matrices and let A be a scalar. Prove that (AA + B)" AAT + BT. d) Let A1,..., An be m x mn matrices. Suppose also that B and C are m x m matrices. Given that B E Span(A1,..., An) and B+C E Span(A1,..., An), show that C E Span(A1,..., An).

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