If V is the subspace spanned by (1,0,1) and (2,1,0), find a matrix A that has V as its row spence. Find a matrix B that has V as its nullspace.

Find two 22 matrices such that |A|+|B|=|A+B|.

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.

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.

In general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that .