Transcribed Text
1  Let P be the plane in R3 with equation of xy3z=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 nullspace and left nullspace 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, nullspace, 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 nullspace.
C. Multiply AB.
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