Give an example of a matrix A such that (1) Ax = b has a solution for infinitely many b e R°, but (2) Ax = b does not have a solution for some b E R°. A =

-1 1 -3 2 2 -3 -2] M³+c₁M² + c₂M + c3I3 = 0, where I3 is the identity 3 x 3 matrix. Let M C1 || C2 = C3 = -3] 3. Find C₁, C₂, and c3 such that 1

Let M = -5 M2 + c, M + c2I, = 0, where I, is the identity 2 x 2 matrix. 3 Find c and c2 such that C1 = C2

Given the matrix A = 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ" Enter each matrix Q and D in the format [[a11 , a12 , a13] , [a21 , a22 , a23] , [a31, a32, a33]]. Note: if you need to enter a square root of a number x you can do it as follows: sqrt (x). Alternatively, you can compute matrix entries in the decimal form rounded to 3 decimal places, and enter them in this. Matrix Q: Matrix D: