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10 Nov 2019
1 2 3 -2 3 1 and B 34 -4-2 I. (20 points) Consider the matrices A (a) Compute AB (b) Compute BA (c) Write each colum of AB as a linear combination of the columns of A (d) Write each column of BA as a linear combination of the columns of B. 2. (20 points) For any nx n matrix A and any positive integerm, define the matrix power Let D = ( 0 2 and let U = ( 0 1 (a) Find D2 and D (b) What is D for general m? (c) Find U and U3 (d) What is U for general m? 3. (20 points) (1.3.30) Let 0 be the 2 x 2 matrix with all zero entries. (a) Does there exist a 2 x 2 matrix A so that A 0, but AA ? Justify your answer (b) Does there exist a 2 Ã 2 matrix A so that A 0, but AA = A? Justify your answer
1 2 3 -2 3 1 and B 34 -4-2 I. (20 points) Consider the matrices A (a) Compute AB (b) Compute BA (c) Write each colum of AB as a linear combination of the columns of A (d) Write each column of BA as a linear combination of the columns of B. 2. (20 points) For any nx n matrix A and any positive integerm, define the matrix power Let D = ( 0 2 and let U = ( 0 1 (a) Find D2 and D (b) What is D for general m? (c) Find U and U3 (d) What is U for general m? 3. (20 points) (1.3.30) Let 0 be the 2 x 2 matrix with all zero entries. (a) Does there exist a 2 x 2 matrix A so that A 0, but AA ? Justify your answer (b) Does there exist a 2 Ã 2 matrix A so that A 0, but AA = A? Justify your answer
Elin HesselLv2
28 Feb 2019