Which of the following subsets of R³X3 are subspaces of R³X³ A. The diagonal 3 x 3 matrices B. The 3 x 3 matrices whose entries are all integers c. The 3 x 3 matrices with all zeros in the second row D. The invertible 3 x 3 matrices - (8) = 5 OF. The 3 x 3 matrices whose entries are all greater than or equal to 0 7 E. The 3 x 3 matrices A such that A 6

C. Let A be an m x n matrix. Then the orthogonal complement (Row (A)) of the row space of A is Nul(A), the null space of A. Select one: O True O False

3. Matrices and vectors a. Compute the following [2 marks] -5x² + 7y² + 2x² + 2xy +8xz - 6yz • -5x² + 7y² + 2z² + 2xy - 6xz+8yz · 5x² + 7y² + 2z² + 2xy +6xz-8yz • 5x² + 7y² + 2z² - 2xy - 6xz+8yz b. What's the inverse of (² (x y z) -5 1 -3 G+90- 1 7 4 -3 4 2 =? ? You should use the definition of inverse and check the conditions for each matrix in turn. [2 marks] 2 2/3 1/31 -1/3 1/3 (12) (-1/3 2/3)

Find the examples that satisfy the statement in the given items and show some work how they are correct examples. (a) A 4 × 4 matrices A that is not digonalizable.(b) Two matrices A and B that have the same characteristic polynomial but are not similar.(c) Two diagonal matrices D1 and D2 that are similar but they are not equal.(d) Two similar matrices A and B such that A is orthogonally digonalizable but B is not orthogonally diagonalizable.