Write each system of linear equations as an augmented matrix:Part (a): 2x-5y=-34x=3y-1Part (b): 4x+3y-2z=-3-2x+y-3z=4-x-4y+5z=-2

Part (a): The augmented matrix is 2-5-34-3-1.Part (b): The augmented matrix is 43-2-3-21-34-1-45-2.

Q. 199 - Intermediate Algebra

Write each system of linear equations as an augmented matrix:

Part (a): $\{\begin{cases} 2 x - 5 y = - 3 \\ 4 x = 3 y - 1 \end{cases}$

Part (b): $\{\begin{cases} 4 x + 3 y - 2 z = - 3 \\ - 2 x + y - 3 z = 4 \\ - x - 4 y + 5 z = - 2 \end{cases}$

Verified

Answer

Part (a): The augmented matrix is $[\begin{array}{r} 2 & - 5 & - 3 \\ 4 & - 3 & - 1 \end{array}]$ .

Part (b): The augmented matrix is $[\begin{array}{cccr} 4 & 3 & - 2 & - 3 \\ - 2 & 1 & - 3 & 4 \\ - 1 & - 4 & 5 & - 2 \end{array}]$ .

1Part (a) Step 1. Given information.

Consider the given system of equations,

$\{\begin{cases} 2 x - 5 y = - 3 \\ 4 x = 3 y - 1 \end{cases}$

Here, the second equation is not in standard form.

Rewrite the second equation in standard form,

$4 x = 3 y - 1 4 x - 3 y = - 1$

2Part (a) Step 2. Write in augmented matrix.

Write the standard form of the second equation,

$\{\begin{cases} 2 x - 5 y = - 3 \\ 4 x - 3 y = - 1 \end{cases}$

Write the augmented matrix,

$[\begin{array}{r} 2 & - 5 & - 3 \\ 4 & - 3 & - 1 \end{array}]$

3Part (b) Step 1. Given information.

Consider the given system of equations,

$\{\begin{cases} 4 x + 3 y - 2 z = - 3 \\ - 2 x + y - 3 z = 4 \\ - x - 4 y + 5 z = - 2 \end{cases}$

Here all the equations are in the standard form.

Write the augmented matrix,

$[\begin{array}{cccr} 4 & 3 & - 2 & - 3 \\ - 2 & 1 & - 3 & 4 \\ - 1 & - 4 & 5 & - 2 \end{array}]$