Exam 47: Matrices and Systems of Equations

Fill in the blank using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { r r r } 2 & 1 & - 2 \\- 10 & - 1 & 9\end{array} \right]$ $\left[ \begin{array} { l l l } 2 & 1 & - 2 \\0 & \square & - 1\end{array} \right]$

The currents in an electrical network are given by the solution of the system​ $\left\{ \begin{aligned}I _ { 1 } - I _ { 2 } + I _ { 3 } & = 5 \\3 I _ { 1 } + 4 I _ { 2 } & = 19 \\I _ { 2 } + 3 I _ { 3 } & = 28\end{aligned} \right.$ ​ where I₁,I₂ and I₃ are measured in amperes.Solve the system of equations using matrices. ​

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}4 x - 9 y - 9 z & = - 74 \\6 x + 8 y - 2 z & = - 22 \\6 x - y + 9 z & = 4\end{aligned} \right.$

The currents in an electrical network are given by the solutions of the system $\left\{ \begin{aligned}I _ { 1 } + I _ { 2 } - I _ { 3 } & = 0 \\4 I _ { 1 } + 5 I _ { 3 } & = 23 \\6 I _ { 2 } + I _ { 3 } & = 9\end{aligned} \right.$ where I₁,I₂,and I₃ are measured in amperes.Solve the system of equations using matrices.

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.​ $\left[\begin{array}{l}{\begin{array}{cccc}1 & 0 & 0 & \vdots8\end{array}} \\\begin{array}{llll}0 & 1 & 0 & \vdots-6\end{array} \\\begin{array}{llll}0 & 0 & 1 & \vdots0\end{array} \\\end{array}\right]$ ​

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. ​​ $\left\{ \begin{array} { r l r } 3 x + 2 y - z + w & = 0 \\x - y + 4 z - w & = 28 \\- 2 x + y + 2 z - w & = 3 \\x + y + z + w & = 8\end{array} \right.$ ​

Solve the system using Gaussian elimination.​ $\left\{ \begin{array} { l } x + y = - 2 \\x + z = - 4 \\y + z = - 4\end{array} \right.$ ​

An augmented matrix that represents a system of linear equations (in variables x,y,and z)has been reduced using Gauss-Jordan elimination.Write the solution represented by the augmented matrix. $\left[\begin{array}{llll}1&0&0&:2\\0 & 1 & 0 & :3 \\0 & 0 & 1 & :4\end{array}\right]$

Solve the system using Gauss-Jordan elimination.​ $\left\{ \begin{aligned}x + y + 2 z + t & = 62 \\x + 2 y + z + t & = 62 \\2 x + y + z + t & = 49 \\x + y + z + 2 t & = 62\end{aligned} \right.$ ​

Select the augmented matrix for the system of linear equations.​ $\left\{ \begin{aligned}6 x - 5 y & = - 7 \\- x + 5 y & = 15\end{aligned} \right.$ ​

Write the system of linear equations represented by the augmented matrix.Then use back-substitution to solve.(Use variables x,y,and z. ) $\left[ \begin{array} { r r r r r } 1 & 9 & - 3 &\vdots& - 39 \\0 & 1 & 2 & \vdots & 0 \\0 & 0 & 1 & \vdots & 2\end{array} \right]$

The currents in an electrical network are given by the solutions of the system $\left\{ \begin{array} { r l r } I _ { 1 } + I _ { 2 } - I _ { 3 } & = 0 \\2 I _ { 1 } + 3 I _ { 3 } & = 37 \\4 I _ { 2 } + I _ { 3 } & = 25\end{array} \right.$ where I₁,I₂,and I₃ are measured in amperes.Solve the system of equations using matrices.

Select the order for the following matrix.​ $\left[ \begin{array} { c c c c } - 3 & 5 & 10 & 0 \\0 & 0 & 5 & 5 \\4 & 4 & 8 & 5\end{array} \right]$ ​

Fill in the blank(s)using elementary row operations to form a row-equivalent matrix.​ $\left[ \begin{array} { c c c c } 1 & 6 & 5 & - 1 \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]$ ​​ $\left[ \begin{array} { c c c c } 1 & 6 & \cdots & \cdots \\0 & 1 & - 2 & 2 \\0 & 0 & 1 & 6\end{array} \right]$ ​

Identify the elementary row operation being performed to obtain the new row-equivalent matrix. Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { r r r } - 9 & - 8 & 6 \\- 8 & - 5 & - 3\end{array} \right]$ $\left[ \begin{array} { r r r } 7 & 2 & 12 \\- 8 & - 5 & - 3\end{array} \right]$

Select the augmented matrix for the system of linear equations.​ $\left\{ \begin{aligned}x + 14 y - 12 z & = 12 \\5 x - 4 y + 5 z & = 0 \\12 x + y & = 9\end{aligned} \right.$ ​

Determine the order of the matrix.​ $\left[ \begin{array} { l l l } 8 & 5 & 4 \\7 & 8 & 1\end{array} \right]$ ​

Identify the elementary row operation being performed to obtain the new row-equivalent matrix. Original Matrix New Row-Equivalent Matrix $\left[ \begin{array} { r r r } - 1 & - 8 & 5 \\- 8 & 9 & 9\end{array} \right]$ $\left[ \begin{array} { r r r } - 17 & 10 & 23 \\- 8 & 9 & 9\end{array} \right]$

Use a system of equations to find the specified equation that passes through the points.Solve the system using matrices. Parabola: y = ax² + bx + c

Fill in the blank using elementary row operations to form a row-equivalent matrix. $\left[ \begin{array} { r r r } - 1 & 5 & - 3 \\- 2 & 1 & 4\end{array} \right]$ $\left[\begin{array}{rrr}-1 & 5 & -3 \\0 & \square & 10\end{array}\right]$