Suppose A E M(R). Write A = (a₁ | |ax). a. A vector x ER is in the null space of A if (select all that apply): DA. 1a1 + + kak = 0₁ B. rref(Ay) has no rows of the form (0...01). Oc.y=z₁a₁ +...+ak for some (₁,...,) E R. D. The dot product of x with every row vector from A is 0. DE. y = Ax for some x E R. OF. y E span{a1,..., ak). OG. Ax = 0,. b. A vector y ER" is in the column space of A if (select all that apply): A. The dot product of x with every row vector from A is 0. OB. y E span{a₁,..., ak). DC. rref (Ay) has no rows of the form (0...01). D.y=Ax for some x € R*. DE ₁a1 + + OF. y = a₁ + OG. Ax=0, kak = 0₁₁ +a for some (₁,..., ) ER*.
Suppose A E M(R). Write A = (a₁ | |ax). a. A vector x ER is in the null space of A if (select all that apply): DA. 1a1 + + kak = 0₁ B. rref(Ay) has no rows of the form (0...01). Oc.y=z₁a₁ +...+ak for some (₁,...,) E R. D. The dot product of x with every row vector from A is 0. DE. y = Ax for some x E R. OF. y E span{a1,..., ak). OG. Ax = 0,. b. A vector y ER" is in the column space of A if (select all that apply): A. The dot product of x with every row vector from A is 0. OB. y E span{a₁,..., ak). DC. rref (Ay) has no rows of the form (0...01). D.y=Ax for some x € R*. DE ₁a1 + + OF. y = a₁ + OG. Ax=0, kak = 0₁₁ +a for some (₁,..., ) ER*.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose A E M₂ (R). Write A = (a₁ | ...
..ak).
a. A vector x ER is in the null space of A if (select all that apply):
DA. 1a1 ++аk = 0₁₁
OB. Tref (Ay) has no rows of the form (0...0 | 1).
OC. y = a₁ + +ak for some (1, ..., x) = R¹.
OD. The dot product of x with every row vector from A is 0.
OE. y = Ax for some x € RA.
OF. y E span{a1,..., ak).
OG. Ax = 0,₁.
b. A vector y ER" is in the column space of A if (select all that apply):
A. The dot product of x with every row vector from A is 0.
OB. y E span{a₁,..., ak}.
OC. rref(Ay) has no rows of the form (0...01).
D. y = Ax for some x € R.
DE ₁a₁ +
+ak = 0,₁
OF. y = 21a₁ +...+a for some (₁,..., ) E R*.
OG. Ax = 0,
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