Solve the following equation using Reduced-Row Echelon Form: 4x1 - 2x2 - 3x3 + x4 = 3 2x1 - 2x2 -...

Question:

Solve the following equation using Reduced-Row Echelon Form:{eq}4x1 - 2x2 - 3x3 + x4 = 3 \\2x1 - 2x2 - 5x3 + 0 = -10 \\4x1 + x2 + 2x3 + x4 = 17 \\3x1 + 0 + x3 + x4 = 12 {/eq}

Solving a System of Three Equations Using Matrix.

Given the following system of equations:

{eq}\displaystyle x_1 \hat{\imath} + y_1\hat{\jmath} + z_1 \hat{k} = a\\ x_2 \hat{\imath} + y_2\hat{\jmath} + z_2 \hat{k} = b\\ x_3 \hat{\imath} + y_3\hat{\jmath} + z_3 \hat{k} = c {/eq}

the equations can be written as a matrix equation:

{eq}\displaystyle A= \begin{bmatrix} x_1 & y_1 & z_1\\ x_2 & y_2 & z_3\\ x_3 & y_3 & z_3 \end{bmatrix} x = \begin{bmatrix} \hat{\imath}\\ \hat{\jmath}\\ \hat{k} \end{bmatrix} B = \begin{bmatrix} a\\ b\\ c \end{bmatrix} {/eq}

To solve for {eq}\hat{\imath}, \hat{\jmath} {/eq} and {eq}\hat{k} {/eq} reduce matrix to row echelon form by performing some row operation.

Answer and Explanation:

The given system of equation is

{eq}\displaystyle 4x_{1} -2x_{2} -3x_{3}+x_{4} =3---------------(1)\\ 2x_{1}-2x_{2}-5x_{3} =...

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How to Solve Linear Systems Using Gaussian Elimination

from Algebra II Textbook

Chapter 10 / Lesson 6
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