P = D = A = Is A diagonalizable over R? choose 4 -3 5 If possible, find an invertible matrix P so that D = P-¹AP is a diagonal matrix. If it is not possible, enter the identity matrix for P and the matrix A for D. You must enter a number in every answer blank for the answer evaluator to work properly. −1 -3 2 3 -1 ✓ Be sure you can explain why or why not.

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.

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

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.

Explain what it means in terms of an inverse for a matrix to have a 0 determinant.

Can a matrix whose entry is 0 on the diagonal be solved? Explain why or why not. What would you do to remedy the situation?

Can we multiply any column matrix by any row matrix? Explain why or why not.

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

True or False? Justify your answer. a) Let A, B, and C be two square matrices of the same dimension and A be an invertible matrix then ((A^−1)BCA)^2023 = A^(−1)xB^(2023)xC^(2023)xA. b) Let A be an n×n matrix. The set of all n×n matrices X that satisfies (A^2 −3I)X = O is not be closed under the matrix addition. (O denotes the zero matrix of the proper dimensions.) c) If A and B are 6×6 matrices of rank 6, then AB also has rank 6.

Diagonalise the matrix: Find a diagonal matrix D & an inverted matrix P such that A= PDP^-1. You don’t have to compute P^-1