-18 [] 12 Let u= 40 and A= 2-4 9 Is u in the plane in R³ spanned by the columns of A? Why or why not? -5 2 2 *** Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) OA. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. B. No, the reduced echelon form of the augmented matrix is which is an inconsistent system.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 48E
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Question
Let u =
- 18
40 and A=
12
2-4
-5
2
9
Is u in the plane in R³ spanned by the columns of A? Why or why not?
2
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or decimal for each matrix element.)
OA. Yes, multiplying A by the vector writes u as a linear combination of the columns of A.
B. No, the reduced echelon form of the augmented matrix is, which is an inconsistent system.
Transcribed Image Text:Let u = - 18 40 and A= 12 2-4 -5 2 9 Is u in the plane in R³ spanned by the columns of A? Why or why not? 2 Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) OA. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. B. No, the reduced echelon form of the augmented matrix is, which is an inconsistent system.
b₁
and b = b₂
4-2
b3
describe the set of all b for which Ax=b does have a solution.
Let A =
1 -2 -1
-2
2 0
2
Show that the equation Ax=b does not have a solution for all possible b, and
How can it be shown that the equation Ax=b does not have a solution for all possible b? Choose the correct answer
below.
OA. Find a vector b for which the solution to Ax=b is the zero vector.
B. Find a vector x for which Ax=b is the zero vector.
C. Row reduce the augmented matrix Ab ]
to demonstrate that
] has a pivot position in every row.
[Ab
D. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row.
E. Row reduce the matrix A to demonstrate that A has a pivot position in every row.
Transcribed Image Text:b₁ and b = b₂ 4-2 b3 describe the set of all b for which Ax=b does have a solution. Let A = 1 -2 -1 -2 2 0 2 Show that the equation Ax=b does not have a solution for all possible b, and How can it be shown that the equation Ax=b does not have a solution for all possible b? Choose the correct answer below. OA. Find a vector b for which the solution to Ax=b is the zero vector. B. Find a vector x for which Ax=b is the zero vector. C. Row reduce the augmented matrix Ab ] to demonstrate that ] has a pivot position in every row. [Ab D. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. E. Row reduce the matrix A to demonstrate that A has a pivot position in every row.
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