(Discrete Math) ### Matrix Equations: Solving for Real NumbersFind real numbers $ a $, $ b $, and $ c $ such that the following are true.#### (a)Given the matrix equation:\[ \begin{bmatrix}a + b & a - c \\c & b - a \end{bmatrix}=\begin{bmatrix}3 & 0 \\1 & 1 \end{bmatrix}\]Solve for $ (a, b, c) $:\[ (a, b, c) = \boxed{\phantom{000}} \]#### (b)Given the matrix equation:\[ \begin{bmatrix}2a & b + c \\c - a & 2b - a \end{bmatrix}=\begin{bmatrix}0 & 7 \\4 & 6 \end{bmatrix}\]Solve for $ (a, b, c) $:\[ (a, b, c) = \boxed{\phantom{000}} \]---**Need Help?** Click on the "Read It" button for additional resources and detailed solutions. [Read It](#)

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Find real numbers a, b, and c such that the following are true. [ (a) а +ba — C 3 0 a 1 1 (а, b, c) 3 [: (b) 2a b + c 0 7 = С — а 2b - a 4 6 (а, b, с) - Need Help? Read It

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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(Discrete Math)

### Matrix Equations: Solving for Real Numbers

Find real numbers $ a $, $ b $, and $ c $ such that the following are true.

#### (a)

Given the matrix equation:
\[
\begin{bmatrix}
a + b & a - c \\
c & b - a
\end{bmatrix}
=
\begin{bmatrix}
3 & 0 \\
1 & 1
\end{bmatrix}
\]

Solve for $ (a, b, c) $:
\[ (a, b, c) = \boxed{\phantom{000}} \]

#### (b)

Given the matrix equation:
\[
\begin{bmatrix}
2a & b + c \\
c - a & 2b - a
\end{bmatrix}
=
\begin{bmatrix}
0 & 7 \\
4 & 6
\end{bmatrix}
\]

Solve for $ (a, b, c) $:
\[ (a, b, c) = \boxed{\phantom{000}} \]

---

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