How would I write a matrix equation for...

0.2x+0.04y-0.2z=-.03

1.1x-0.6y+0.7z=0.5

0.25x+0.3y-0.35z=0.1

Would you be able to explain WHY you are doing your particular steps (my book offers explanations for similar problems, but I do not understand why each step takes place)

Thanks for your help

~Shel

you would have a 3x3 matrix

.2 .04 .2
1.1 .5 .7
.25 .3 35
multiplied by the column matrix
x
y
z
and equal that to the column matrix

.03
.5
.1

I assume you know how to multiply one matrix by another.

To write a matrix equation for the given system of equations, we need to translate the coefficients and variables into a matrix form. Here's a step-by-step explanation:

Step 1: Identify the variables.
In this case, the variables present are x, y, and z.

Step 2: Write down the coefficients and constants.
The coefficients in front of x, y, and z, respectively, are:
Equation 1: 0.2, 0.04, -0.2
Equation 2: 1.1, -0.6, 0.7
Equation 3: 0.25, 0.3, -0.35

The constants on the right side of the equations are:
Equation 1: -0.03
Equation 2: 0.5
Equation 3: 0.1

Step 3: Arrange the coefficients and variables into a matrix form.
To do this, we'll create a coefficient matrix (A) containing the coefficients of the variables (x, y, and z), a variable matrix (X) containing the variables themselves, and a constant matrix (B) containing the constants on the right side of the equations.

A = | 0.2 0.04 -0.2 |
| 1.1 -0.6 0.7 |
| 0.25 0.3 -0.35 |

X = | x |
| y |
| z |

B = | -0.03 |
| 0.5 |
| 0.1 |

Step 4: Write the matrix equation.
To write the matrix equation, we need to use matrix multiplication. The equation will be in the form AX = B.

So, A * X = B

| 0.2 0.04 -0.2 | | x | | -0.03 |
| 1.1 -0.6 0.7 | * | y | = | 0.5 |
| 0.25 0.3 -0.35 | | z | | 0.1 |

This matrix equation represents the given system of equations.

Each step is necessary to organize and represent the given system of equations in a matrix form. By doing so, we can work with matrix operations and solve the system of equations more efficiently.