Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

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

If A and B are matrices and AB=0, msut |A|=0 or |B|=0? Explain.

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.

Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why not. For simplicity, assume a 22 matrix.

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

Find ATA for the matrix A=[531246]. Show that this product is symmetric.

Solve for x,y,z and w in the matrix equation wxyx=-432-1+2ywzx.

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

Can you explain whether a 2×2 matrix with an entire row of zeros can have an inverse?