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1- - Let P be the plane in R3 with equation of x-y-3z=6. - - a. Find two vectors in P and check whether their sum and subtraction are in P or not? Let Po be the plane through (0,0,0) parallel to P. b. What is the equation of Pó? C. Find two vectors in Po and check whether their sum and subtraction are in Po or not? d. Which one (P or Po or both) is a subspace of R3? 2- Find the reduced row Echelon form R for each of these matrices: = 3- Find the null-space and left null-space of matrices A, B, C, and D in problem 2. 4- Find the complete solution x x x x p x x by forward elimination on [A b]: X1 A= - X3 2352 X4 5- Find a basis for each of the four subspaces (column space, row space, null-space, left null- space) associated with A: 2 3 4 00082 6- If V is the subspace spanned by (1,1,1) and (2,1,0): a. Find a matrix A that has V as its row space. b. Find a matrix B that has V as its null-space. C. Multiply AB.

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