3. Consider a matrix equation Ax = b, where A [18] b = 20 Let a22 2 . new matrix as A' = = a11 a12 a13 +0.001] a22 0 a11 a23 0 a33 Hint: Cramer's Rule tells us the formula for the (unique) solution to a linear system. a12 a13 a22 a23 X = 0 a33 1000, and suppose that det(A) = 1. If we add 0.001 to a13 and denote the 2 what is the solution x' of A'x' X1 X2 and X3 = b in terms of x?

= 1) Suppose that A² A and B is a diagonal matrix similar to A. Prove that B² = B and that the entries on the diagonal of B are only 0 and 1.

1. Indicate whether each statement is true or false. No justification is necessary.

O Given C' - = 데 2 find CCT. This is a Matrix multiplication of C with the transpose of C