For this quiz, you may use: https://matrixcalc.org/ Show all…
For this quiz, you may use: https://matrixcalc.org/ Show all work, provide justifications when needed. Q1. Let (6 points) (a) Find a basis for Col(A) (b) Find a basis for Nul(A) (c) Find a basis for Row(A) = Col(AT) Q2. Chose any vector in Nul(A) and verify (this means compute the product) (2 points) Q3. Chose any vector in Col(A) and verify that (2 points) Q4. Explain why we get the result we do in Q3 (you could state a Theorem if you know one, but I am suggesting use the fact that matrix multiplication is a linear transformation together with properties of linear transformations). (2 points) Q5. What is the rank of the matrix A? (1 point) Q6. What is the dimension of Col (A) ? (1 point) Q7. What is the dimension of Nul (A)? (1 point) Q8. Suppose A is an