Algebra - Augmented Matrices (Practice Problems)

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Section 7.3 : Augmented Matrices

For the following augmented matrix perform the indicated elementary row operations. [4−1350259−61−310]
1. $8{R_{\,1}}$
2. ${R_{\,2}} \leftrightarrow {R_{\,3}}$
3. ${R_{\,2}} + 3{R_{\,1}} \to {R_{\,2}}$
Solution
For the following augmented matrix perform the indicated elementary row operations. [1−6202−81043−4−12]
1. $\frac{1}{2}{R_{\,2}}$
2. ${R_{\,1}} \leftrightarrow {R_{\,3}}$
3. ${R_{\,1}} - 6{R_{\,3}} \to {R_{\,1}}$
Solution
For the following augmented matrix perform the indicated elementary row operations. [10−1−51407−107−23]
1. $- 9{R_{\,3}}$
2. ${R_{\,1}} \leftrightarrow {R_{\,2}}$
3. ${R_{\,3}} - {R_{\,1}} \to {R_{\,3}}$
Solution

Note : Problems using augmented matrices to solve systems of equations are in the next section.