Question

please solve parts a, b, c for this question

1 A = -1 1 (a) Suppose that is any nonzero vector in R2. Explain why the vectors U, AU, and A2 must be linearly dependent. (Note: do not use any numerical examples in your answer; your reasoning must be valid no matter what is.) s in the cpak of the ImlA) Thuscan be uvi Hen os a linear combo of the basi vetus op im{A) (b) Let Part (a) shows that there are scalars co, C, and o such that Go+CA+oA-6. (1) Explain why this shows that the matrix col +eA+ o42 is not invertible. Co 7-0 +C2 (c) Let Find scalars Co. C, and c2 such that (1) holds. Box your answer Co Co-4

Answer 1

a)We know that dimension of R2 linearly independent set will have 2 elements so any set containing than two elements will be linearly dependent and in this case , Av, Au dependent over R is 2. which means that maximal more v are

b)Let T T()0 and here CO+C1AC2A 0, so T is not one one and hence not invertible.

c) image attached

If you need any further clarification regarding this problem feel free to comment below

A 2 A v -1 3 4 2 -4 A V t C2 Co t Cot C O CET-C1-4C, = 0 C2 = ombruaton is pasui ble po a h =