For each of the following, identify whether the statement is true or false. No explanation is necessary. a. If A E R"mxn, then dim Nul A + rank A = n. b. A set of vectors {v1,V2, V3} is linearly dependent if the only solution to az V1 + A2V2 + azV3 = 0 is the trivial solution. Let A E RmXn, If Ax = b for some x E R", then b E Col A. d. Consider AE RmXn and BE R"XP. The ith column of AB is a linear combination of the C. columns of B.
For each of the following, identify whether the statement is true or false. No explanation is necessary. a. If A E R"mxn, then dim Nul A + rank A = n. b. A set of vectors {v1,V2, V3} is linearly dependent if the only solution to az V1 + A2V2 + azV3 = 0 is the trivial solution. Let A E RmXn, If Ax = b for some x E R", then b E Col A. d. Consider AE RmXn and BE R"XP. The ith column of AB is a linear combination of the C. columns of B.
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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On #7 and #8
Transcribed Image Text:State for each whether that means that A is
"invertible" or
"not invertible".
a. The columns of A form a basis for R".
b. det A = 0.
%3D
C.
There is a nontrivial solution to Ax = 0.
d. rank A = n.
7. For each of the following, identify whether the statement is true or false. No explanation is
necessary.
a. If A E Rmxn, then dim Nul A + rank A = n.
b. A set of vectors {v1,V2, V3} is linearly dependent if the only solution to
a, V1 + azV2 + azV3 = 0
is the trivial solution.
Let A E RmX", If Ax b for some x E R", then b E Col A.
d. Consider AE RmXn and BE R"XP. The ith column of AB is a linear combination of the
C.
columns of B.
[1
8. Find the inverse of A =3
21
-2
4. Show all work and clearly label A-.
01
1
1
0.
-2
9. Find the determinant of A =-3
Show all
41
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