Suppose that the augmented matrix for a linear system in the unknowns x1, x2, 23, X4 and x, have been reduced by elementary row operations to 1 0. -2 -3 0 a 1 7 3 - a 0 0 0. 1 31 – 5a 0 0 2a 7 (a) Given that this linear system is consistent, find the value of a. (b) Solve the system.
Suppose that the augmented matrix for a linear system in the unknowns x1, x2, 23, X4 and x, have been reduced by elementary row operations to 1 0. -2 -3 0 a 1 7 3 - a 0 0 0. 1 31 – 5a 0 0 2a 7 (a) Given that this linear system is consistent, find the value of a. (b) Solve the system.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![Suppose that the augmented matrix for a linear system in the unknowns \( x_1, x_2, x_3, x_4, \) and \( x_5 \) has been reduced by elementary row operations to:
\[
\begin{bmatrix}
1 & 0 & -2 & -3 & 0 & a \\
0 & 1 & 4 & 7 & 0 & 3 - a \\
0 & 0 & 0 & 0 & 1 & 31 - 5a \\
0 & 0 & 0 & 0 & 0 & 2a - 7
\end{bmatrix}
\]
(a) Given that this linear system is consistent, find the value of \( a \).
(b) Solve the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1b54d61-1255-406a-9b79-99af3ebb60e9%2F4bf6fa09-c125-402c-b08e-7f5b554ad9e3%2Fizm66f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that the augmented matrix for a linear system in the unknowns \( x_1, x_2, x_3, x_4, \) and \( x_5 \) has been reduced by elementary row operations to:
\[
\begin{bmatrix}
1 & 0 & -2 & -3 & 0 & a \\
0 & 1 & 4 & 7 & 0 & 3 - a \\
0 & 0 & 0 & 0 & 1 & 31 - 5a \\
0 & 0 & 0 & 0 & 0 & 2a - 7
\end{bmatrix}
\]
(a) Given that this linear system is consistent, find the value of \( a \).
(b) Solve the system.
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