Exam 47: Matrices and Systems of Equations

Select the system of linear equations represented by the following augmented matrix.(Variables x,y,z,and w are used whenever applicable. )​ $\left[ \begin{array} { c c c l } 1 & 3 & :8 \\3 & -4 & :5\end{array} \right]$ ​

Determine the order of the matrix.​ $\left[ \begin{array} { l l l } 4 & 3 & - 8\end{array} \right]$ ​

Identify the elementary row operation being performed to obtain the new row-equivalent matrix. ​ Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { c c c } - 4 & 6 & 1 \\4 & - 1 & - 9\end{array} \right]$ $\left[ \begin{array} { c c c } 20 & 0 & - 53 \\4 & - 1 & - 9\end{array} \right]$ ​

Select the system of linear equations represented by the following augmented matrix.​ $\left[ \begin{array} { r r r } 9 & - 6 & \vdots & 0 \\7 & 4 & \vdots & - 3\end{array} \right]$ ​

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.​ $\left\{ \begin{array} { l } 2 x + 6 y = 10 \\2 x + 3 y = 7\end{array} \right.$ ​

Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. )​ $\left[ \begin{array} { c c c c } 1 & 7 & \vdots & 0 \\0 & 1 & \vdots & - 1\end{array} \right]$ ​

An augmented matrix that represents a system of linear equations (in variables x,y,z and w if applicable)has been reduced using Gauss-Jordan elimination.Find the solution represented by the augmented matrix.​ $\left[\begin{array}{l}{\begin{array}{cccc}1 & 0 & 0 & \vdots-3\end{array}} \\\begin{array}{llll}0 & 1 & 0 & \vdots-9\end{array} \\\begin{array}{llll}0 & 0 & 1 & \vdots3\end{array} \\\end{array}\right]$ ​

Find the system of linear equations represented by the augmented matrix.Then use back substitution to solve.(Use variables x,y,z,and w if applicable. )​ $\left[\begin{array}{lll}1 & -4 & \vdots 6\\0 & 1 & \vdots -5\\\end{array} \right]$ ​

Write the matrix in reduced row-echelon form. $\left[ \begin{array} { r r r r } 5 & - 7 & - 3 & 6 \\- 6 & - 6 & 2 & - 44 \\2 & - 4 & - 2 & - 4\end{array} \right]$

Use the matrix capabilities of a graphing utility to reduce the augmented matrix corresponding to the system of equations,and solve the system.​ $\left\{ \begin{aligned}x + 2 y + 2 z + 4 w & = 20 \\3 x + 6 y + 5 z + 12 w & = 53 \\x + 3 y - 3 z + 2 w & = - 18 \\6 x - y - z + w & = - 30\end{aligned} \right.$ ​

Perform the sequence of row operations on the following matrix. Add R₃ to R₄.​ $\left[ \begin{array} { c c } 7 & 1 \\0 & 2 \\- 3 & 4 \\4 & 1\end{array} \right]$ ​

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.​ $\left\{ \begin{aligned}x - 3 z & = - 7 \\3 x + y - 2 z & = 2 \\2 x + 2 y + z & = 4\end{aligned} \right.$ ​

Perform the sequence of row operations on the following matrix. Add -3 times R₁ to R₂.​ $\left[ \begin{array} { c c c } 1 & 3 & 4 \\3 & - 1 & - 5 \\4 & 1 & - 1\end{array} \right]$ ​

Use matrices to find the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.​ $\left\{ \begin{aligned}5 x - 5 y & = 5 \\- 2 x - 3 y & = 18\end{aligned} \right.$ ​

Select the system of linear equations represented by the following augmented matrix.​ $\left[\begin{array}{l}{\begin{array}{lllr}2 & 0 & 4 & \vdots-13\end{array}} \\\begin{array}{lllr}0 & 1&-2 & \vdots 6\end{array} \\\begin{array}{lllr}5 & 3 & 0 & \vdots 2\end{array} \\\end{array}\right]$ ​

Write the augmented matrix for the system of linear equations. $\left\{ \begin{aligned}x - 3 y - 2 z & = - 2 \\4 y + 4 z & = 4 \\x + 4 z & = - 2\end{aligned} \right.$

Determine whether the matrix is in row-echelon form.If it is,determine if it is also in reduced row-echelon form. $\left[ \begin{array} { r r r r } 1 & 9 & - 9 & - 6 \\0 & 1 & 0 & - 2 \\0 & 0 & 1 & 1\end{array} \right]$

Write the system of linear equations represented by the augmented matrix.(Use variables x,y,z,and w. ) $\left[\begin{array}{l}{\begin{array}{lllll}-1 & 0 & 0 &3&\vdots2\end{array}} \\\begin{array}{lllll}-7 & 4 & 0 &0& \vdots8\end{array} \\\begin{array}{lllll}0 & 5 & 3 &-5& \vdots-8\end{array} \\\begin{array}{lllll}0 & 0 & -1 &-9& \vdots9\end{array} \\\end{array}\right]$

Select the order for the following matrix.​ $\left[ \begin{array} { l l l l } 5 & - 4 & 3 & 3\end{array} \right]$ ​

Identify the elementary row operation being performed to obtain the new row-equivalent matrix. ​ Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\- 5 & 4 & 9\end{array} \right]$ $\left[ \begin{array} { r r r } 4 & - 1 & - 5 \\11 & 0 & - 11\end{array} \right]$ ​