[ 2 4 -2 11 4. (20pts) Consider a matrix A = 3 7 -8 6 and corresponding Col A & Nul A. -2 -5 7 3 Col A is a subspace of Rk and Nul A is a subspace of R'. |(1) Find k and one nonzero-vector in Col A. | (2) Find 1 and one nonzero-vector in Nul A.
2. * Let A be an m xn matrix, let Col(A) be the column space of A, and let Nul(A) be the null space of A. (a) Show that Nul(A) is a subspace of R". (b) Show that Col(A) is a subspace of RM
11 O-I-1 6 2 3 4. LetA=(1 2 3 4) 5 67 8 15 in Nul)? Explain. a. Is 14 -23 in Nul(A)? Explain. b. Is in Col(A)? Explain. c. Is 10 5. Let A =(2 2 a. Find the characteristic polynomial of A.
Please solve it with clear explanation including the theorem 8.(1) Let w be any nonzero vector in Rº and let V= xERIx. w=0}. Prove or disprove that V is a subspace of Rº. (Prove or disprove) (2) Let W={(x,y,z) ER?\x+2y+32=1}. Prove or disprove that W is a subspace of R. (Prove or disprove)
2) Given 1 3 4 01 A2 4 -5 4 -3 1 -5 0 3 2 By result of Q1, (a) Verify that both Row(A) and Row(A) are subspaces of R5 (b) Verify that Col(A) is a subspace of , 4. Find the Row(A), Col(A) and Null(A) 1) Find the Row(A), Col(A) and Null(A) 1 3 -4 0 1 A 2 4 5 34 1 -5 0 -3 2 -3 1 8 3 -4 2) Given 1 3-4 0 1...
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 10 3 0 0 1 -1 6 5 3 0 1 -3 0 -7 -2 0 -6 1 -2 0 0 0 1 -2 9 1-9 0 0 0 0 0 (a) Find p, q, r s t Nul A, Col A, Row A is a subspace of RP, R9, R', respectively Answer. p = 9= (b) Find a basis for Nul...
Suppose an 8 x 10 matrix A has eight pivot columns. Is Col A=R8? Is Nul A=R2? Explain your answers. Is Col A =R8? A. Yes. Since A has eight pivot columns, dim Col A is 8. Thus, Col A is an eight-dimensional subspace of R8, so Col A is equal to R8 OB. No, the column space of Ais not R. Since A has eight pivot columns, dim Col A is 0. Thus, Col A is equal to 0....
4 1 1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 10 3 0 0 1 -1 6 5 3 0 1 -3 0 -7 -2 0 -6 1 -2 0 0 0 1 -2 91-9 0 0 0 0 0 (a) Find p, q, rs. Nul A, Col A, Row A is a subspace of R", R9, R', respectively Answer. p = 9=- (b) Find a basis for Nul A (c) Find...
1. The matrix A and it reduced echelon form B are given below. 1-2 95 4 [1 0 3 0 0 1 -1 6 5 -3 A= 0 1 -3 0 -7 -B= -2 0 -6 1 -2 0 0 0 1 -2 4 9 -9 0 0 0 0 0 (a) Find p, q, rs. Nul A, Col A, Row A is a subspace of R”, R9, R", respectively Answer.p = 9. r = (b) Find a basis for...
Problem 9. (1 point) T -5 10 1 Let A= and w= 2 -4 Is w in Col(A)? Type "yes" or "no". Is w in Nul(A)? Type "yes" or "no". Note: You can earn partial credit on this problem.