Let A = - 4 2-1 N-E and b = which Ax = b does have a solution. Show that the equation Ax = b does not have a solution for some choices of b, and describe the set of all b for How can it be shown that the equation Ax = b does not have a solution for some choices of b? A. Find a vector b for which the solution to Ax = b is the identity vector. B. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. C. Find a vector x for which Ax = b is the identity vector. D. Row reduce the augmented matrix [A b] to demonstrate that [A b] has a pivot position in every row. E. Row reduce the matrix A to demonstrate that A has a pivot position in every row. Describe the set of all b for which Ax = b does have a solution. The set of all b for which Ax = b does have a solution is the set of solutions to the equation 0 = ☐ b₁+b2 (Type an integer or a decimal.)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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Let A =
- 4
2-1
N-E
and b =
which Ax = b does have a solution.
Show that the equation Ax = b does not have a solution for some choices of b, and describe the set of all b for
How can it be shown that the equation Ax = b does not have a solution for some choices of b?
A. Find a vector b for which the solution to Ax = b is the identity vector.
B. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row.
C. Find a vector x for which Ax = b is the identity vector.
D. Row reduce the augmented matrix [A b] to demonstrate that [A b] has a pivot position in every row.
E. Row reduce the matrix A to demonstrate that A has a pivot position in every row.
Describe the set of all b for which Ax = b does have a solution.
The set of all b for which Ax = b does have a solution is the set of solutions to the equation 0 = ☐ b₁+b2
(Type an integer or a decimal.)
Transcribed Image Text:Let A = - 4 2-1 N-E and b = which Ax = b does have a solution. Show that the equation Ax = b does not have a solution for some choices of b, and describe the set of all b for How can it be shown that the equation Ax = b does not have a solution for some choices of b? A. Find a vector b for which the solution to Ax = b is the identity vector. B. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. C. Find a vector x for which Ax = b is the identity vector. D. Row reduce the augmented matrix [A b] to demonstrate that [A b] has a pivot position in every row. E. Row reduce the matrix A to demonstrate that A has a pivot position in every row. Describe the set of all b for which Ax = b does have a solution. The set of all b for which Ax = b does have a solution is the set of solutions to the equation 0 = ☐ b₁+b2 (Type an integer or a decimal.)
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