I need all details. Thx 2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
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 N A= 2 -5 2 - 2 - 4 - 1 7 -23 -3 -6 -8 17 4 3 6 10 - 19 0 B= [122-5 2 0 0 1 -1 -5 000 0 - 4 000 0 0 rank A= dim Nul A A basis for Col Ais...
If the null space of a 7 x8 matrix is 2-dimensional, find rank A, dim RowA, and dim Col A OA rank A-5, dim Row A 5, dim Col A 5 OB. rank A 6, dim Row A-6, dim Col A 2 OC. rank A-6, dim Row A-6, dim Col A-6 OD. rank A 6, dim Row A 2, dim Col A-2
7. Let A be a 5 x 5 matrix such that 1 2 .40 3 3 6 0 9 3 • det(A+15) = 0 • Nul(A) is 3 dimensional. (a) (5 points) What is rank(A)? Explain the reason why. (b) (5 points) What are the cigenvalues of A? (c) (5 points) Write down the characteristic polynomial of A. (d) (5 points) Is A diagonalizable? Why or Why not?
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....
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 3 -5 -7 2 1 3 -5 - 7 N -2 -6 12 16 -9 0 0 1 1-5 A= B = 2 6 -16 - 20 34 0 0 0 0 5 -3 -9 6 12 0 0 0 0 0 0 rank A= dim Nul A= A...
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...
5. (4) Construct (if possible) a matrix satisfying both conditions below. If not, explain why (a) The null space consists of all linear combinations of (2,2,-1,0) and (-2, 1,0,1) (b) The column space contains (1, 1,0, 1) and (0, 1, 1,-1) and whose null space contains (1,0,1,1) and (0,1,-1,0)7 5. (4) Construct (if possible) a matrix satisfying both conditions below. If not, explain why (a) The null space consists of all linear combinations of (2,2,-1,0) and (-2, 1,0,1) (b) The...
9. (2 pts per part) Let A be an m x n matrix, where m > n, and suppose that the rank of A is n (i.e., A has full column rank). Briefly justify your answers to each question below. a. Which two of the following statements are true? i. There are no vectors in Nul(A). ii. There is no basis for Nul(A). iii. dim(Nul(A)) = 0 iv. dim(Nul(A)) = m – n b. Are the columns of A a...