For the given matrix A, find k such that Nul A is a subspace of and find m such that Col A is a subspace of 1-2 11) A = 0 -4 -1 -3 3 -5 6 5 A) k = 5, m = 2 B) k = 5, m = 5 C) k = 2, m = 5 (D) k = 2, m = 2

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.

Show that the matrix below does not have an LU factorization. A=0110

Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the same for each product but varies by warehouse because of the distances involved. It costs $0.75 to distribute one unit from warehouse 1 and $1.00 to distribute one unit from warehouse 2. Organize these costs into a matrix C and then use matrix multiplication to compute the total cost of distributing each product.

Use an example chosen from 22 matrices to show that for nn matrices A and B,ABBA but AB=BA.

Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of B and the column vectors of AB are in the column space of A.

Determine if the statement is true or false. If the statement is false, then correct it and make it true. A 75 matrix has 5 rows.

Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector space?

Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.