Q 1 Q 2 Find the dimensions of the following linear spaces. (a) P 4 (b) The spac
ID: 3007281 • Letter: Q
Question
Q 1
Q 2
Find the dimensions of the following linear spaces.
(a) P4
(b) The space of all diagonal 6×6 matrices
(c) R5×3
Q 3
Which of the following subsets of P2 are subspaces of P2?
A. {p(t) | p(0)=p(2)}
B. {p(t) | 10p(t)dt=0}
C. {p(t) | p(7)=0}
D. {p(t) | p(t)+8p(t)+6=0}
E. {p(t) | p(5)=2}
F. {p(t) | p(t) is constant }
A. {(x,y,z) | x,y,z>0}
B. {(x,y,z) | 9x+7y=0,4x+6z=0}
C. {(x,y,z) | x+y+z=0}
D. {(x,x9,x7) | x arbitrary number }
E. {(x,y,z) | x+y+z=6}
F. {(6x,2x,3x) | x arbitrary number }
Explanation / Answer
Which of the following sets are subspaces of R3?
A. {(x,y,z) | x,y,z>0} this is not a subspace since does not contain zero vector
B. {(x,y,z) | 9x+7y=0,4x+6z=0} this is a subspace since does contain zero vector
C. {(x,y,z) | x+y+z=0} this is a subspace since does contain zero vector
D. {(x,x9,x7) | x arbitrary number } no , since not closed under addition
E. {(x,y,z) | x+y+z=6} this is not a subspace since does not contain zero vector
F. {(6x,2x,3x) | x arbitrary number } no , since not closed under addition
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