Given: x1 + x2 - 3x3 = 1 -x1 + 2x2 = 1 x1 - x2 + x3 = 2 Which of the following is the coefficient matrix of the given linear system? A. [1 1 3; -1 2 1; 1 1 2] B. [1 1 -3; -1 2 0; 1 -1 1] C. [1 3 1; -1 2 1; 1 1 2] D. [1 1 3; 1 2 1; 1 1 2]
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Equation 1: 4x + 2x^2 - 3x^3 = 0 Coefficients: 4, 2, -3 Equation 2: -x + 2x^2 = 0 Coefficients: -1, 2, 0 Equation 3: 4 - x^2 + 4 = 2 Coefficients: 0, -1, 0 ** Show more…
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In Exercises 49–52, use matrix multiplication to determine whether each matrix is a solution of the system of equations. Use a graphing utility to verify your results. $$ \begin{array}{l}{\left\{\begin{array}{c}{x+2 y=4} \\ {3 x+2 y=0}\end{array}\right.} \\ {\begin{array}{ll}{\text { (a) }\left[\begin{array}{c}{2} \\ {1}\end{array}\right]} & {\text { (b) }\left[\begin{array}{r}{-2} \\ {3}\end{array}\right]} \\ {\text { (c) }\left[\begin{array}{r}{-4} \\ {4}\end{array}\right]} & {\text { (d) }\left[\begin{array}{r}{2} \\ {-3}\end{array}\right]}\end{array}}\end{array} $$
Linear Systems and Matrices
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A. Write each linear system as a matrix equation in the form $A X=B$ B. Solve the system using the inverse that is given for the coefficient matrix. $$ \left\{\begin{aligned} w-x+2 y &=-3 \\ x-y+z &=4 \\ -w+x-y+2 z &=2 \\ -x+y-2 z &=-4 \end{aligned}\right. $$
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In each of the following, express the matrix equation as a system of linear equations. (a) $\left[\begin{array}{ccc}3 & -1 & 2 \\ 4 & 3 & 7 \\ -2 & 1 & 5\end{array}\right]\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}\right]=\left[\begin{array}{c}2 \\ -1 \\ 4\end{array}\right]$ $$ \text { (b) }\left[\begin{array}{cccc} 3 & -2 & 0 & 1 \\ 5 & 0 & 2 & -2 \\ 3 & 1 & 4 & 7 \\ -2 & 5 & 1 & 6 \end{array}\right]\left[\begin{array}{l} w \\ x \\ y \\ z \end{array}\right]=\left[\begin{array}{l} 0 \\ 0 \\ 0 \\ 0 \end{array}\right] $$
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