The matrix set up for the linear equation \begin{cases} 3x + 5y + z = 9 \\ 7x - 2y = 3 + 4z \\ -6x + 3z + 5 = 2z \end{cases} is \begin{bmatrix} 3 & 5 & 1 & 9 \\ 7 & -2 & 3 & 4 \\ -6 & 3 & 5 & 2 \end{bmatrix} True False
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We will have a coefficient matrix A, a variable matrix X, and a constant matrix B. The coefficient matrix A will be: 3 5 0 T -2 0 6 0 5 The variable matrix X will be: x y w The constant matrix B will be: 7 3 + 42 22 Show more…
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Use the augmented matrices $\mathbf{A}, \mathbf{B}, \mathbf{C},$ and $\mathbf{D}$ to answer true or false. $$A=\left[\begin{array}{ll|l}6 & -4 & 2 \\5 & -2 & 7\end{array}\right] \quad B=\left[\begin{array}{ll|l}5 & -2 & 7 \\6 & -4 & 2\end{array}\right] \quad \mathbf{C}=\left[\begin{array}{ll|l}1 & -\frac{2}{3} & \frac{1}{3} \\5 & -2 & 7\end{array}\right] \quad \mathbf{D}=\left[\begin{array}{rr|r}5 & -2 & 7 \\-12 & 8 & -4\end{array}\right]$$ The matrix $\mathbf{A}$ is a $2 \times 3$ matrix.
Systems of Linear Equations and Inequalities
Solving Systems of Linear Equations by Using Matrices
Use the augmented matrices $\mathbf{A}, \mathbf{B}, \mathbf{C},$ and $\mathbf{D}$ to answer true or false. $$A=\left[\begin{array}{ll|l}6 & -4 & 2 \\5 & -2 & 7\end{array}\right] \quad B=\left[\begin{array}{ll|l}5 & -2 & 7 \\6 & -4 & 2\end{array}\right] \quad \mathbf{C}=\left[\begin{array}{ll|l}1 & -\frac{2}{3} & \frac{1}{3} \\5 & -2 & 7\end{array}\right] \quad \mathbf{D}=\left[\begin{array}{rr|r}5 & -2 & 7 \\-12 & 8 & -4\end{array}\right]$$ Matrix $\mathbf{A}$ is equivalent to matrix $\mathbf{C}$.
Use the augmented matrices $\mathbf{A}, \mathbf{B}, \mathbf{C},$ and $\mathbf{D}$ to answer true or false. $$A=\left[\begin{array}{ll|l}6 & -4 & 2 \\5 & -2 & 7\end{array}\right] \quad B=\left[\begin{array}{ll|l}5 & -2 & 7 \\6 & -4 & 2\end{array}\right] \quad \mathbf{C}=\left[\begin{array}{ll|l}1 & -\frac{2}{3} & \frac{1}{3} \\5 & -2 & 7\end{array}\right] \quad \mathbf{D}=\left[\begin{array}{rr|r}5 & -2 & 7 \\-12 & 8 & -4\end{array}\right]$$ Matrix $\mathbf{B}$ is equivalent to matrix $\mathbf{A}$.
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