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+ Question Details 2 1 , and A = | V1 V2 V3 | . Is p in Nul A? Let v,-| 0 2 Yes, p is in Nul A No, p is not in Nul A 5.+ Question Details 2 2 10 2 1 0 30 0 2 41 4 2 16 3 Let A so that an echelon form of A is given by . Find a basis for Col A 1 0 3 1 0 0 0...
Determine the dimensions of Nul A and Col A for the matrix shown below. 1 4 -4 3-3 6 - 1 0 0 0 0 00 0 A= 0 0 0 0 0 0 0 0 0 0 0 0 0 0 The dimension of Nul A is and the dimension of Col A is
Determine the dimensions of Nul A and Col A for the matrix shown below. 1 5 9 0 7 6 3 A= 0 1 4 0 4 2 5 The dimension of Nul A is and the dimension of Col A is
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...
5 1 -2 0-4 Let A=0 0 0 0 13 1 -2 0 -3 5 a. Find a basis for Col A and find Rank A. b. Find a basis for Nul A.
a) If A is a 3 x 6 matrix and Rank(A) = 2, then what is the dimension of Nul(A)? b) If B is a 8 x 5 matrix and the dimension of Nul(B) = 3, what is the dimension of Col(B)? c) If C is a 4 x 8 matrix, what is the largest possible dimension of Row(C)?
Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A. Then find bases for Col A. Row A, and Nul A. 1 1 -2 0 -2 -2 1 1 0 1 -1 0 - 1 1 A= 1 - 1 1 -2 0 -2 -2 2-3 0-3 - 1 0 0 -3 -10 1 - 2 21 5 -2 1 - 1 00 B 1 1 4 3 0 0 00...
Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A. Then find bases for Col A, Row A, and Nul A. 1 2-2 4-5 1 2-2 -4 -5 00 1 -4 0 0 0 05 3 6 -814-12 -3 -6 14 20 0 rank A 3 dim Nul A= 2 2 812 A basis for Col A is 2 -314 (Use a comma to separate vectors as needed.) 2 A basis...
Consider 01 0 A 1 20 4 (a) Find a basis for Row A and Nul A and hence find the dimension of each. (b) Is (-2,1,1) in Nul A? Justify your answer. Consider 01 0 A 1 20 4 (a) Find a basis for Row A and Nul A and hence find the dimension of each. (b) Is (-2,1,1) in Nul A? Justify your answer.
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.