Compute the rank of the following matrix. Show all work. 1 -1 2 -1 -1 0 -1 2 2 -460

Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be used to create a leading 1 at the top of the first column. Which do you prefer and why?

Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]

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

15. Reverse the elementary row operations used in Example 2.9 to show that we can convert

Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.

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

Use elementary matrices to find the inverse of A=1a0010001100b1000110001000c, c0.

Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Write the third column of the matrix as a linear combination of the first two columns if possible. [102422751]