I have to solve these using matrices by hand. Can someone please help me?

2x-3y-2z=4
(1/4)x-(2/5)y+(3/4)z=(-1/3)
-2x+1.3y-3z=5

Thank you so much! :)

2x-3y-2z=4

(1/4)x-(2/5)y+(3/4)z=(-1/3)
-2x+1.3y-3z=5
==============================
Google Gauss Jordan reduction

use all integers or fractions
2 -3 -2 4
1/4 -2/5 3/4 -1/3
-2 13/10 -3 5

Divide row 1 by 2
1 -3/2 -1 2
1/4 -2/5 3/4 -1/3
-2 13/10 -3 5

Add (-1/4 * row1) to row2
1 -3/2 -1 2
0 -1/40 1 -5/6
-2 13/10 -3 5

Add (2 * row1) to row3
1 -3/2 -1 2
0 -1/40 1 -5/6
0 -17/10 -5 9

Divide row2 by -1/40
1 -3/2 -1 2
0 1 -40 100/3
0 -17/10 -5 9

Add (17/10 * row2) to row3
1 -3/2 -1 2
0 1 -40 100/3
0 0 -73 197/3

Divide row3 by -73
1 -3/2 -1 2
0 1 -40 100/3
0 0 1 -197/219

Add (40 * row3) to row2
1 -3/2 -1 2
0 1 0 -580/219
0 0 1 -197/219

Add (1 * row3) to row1
1 -3/2 0 241/219
0 1 0 -580/219
0 0 1 -197/219

Add (3/2 * row2) to row1
1 0 0 -629/219
0 1 0 -580/219
0 0 1 -197/219

I used this:

http://www.gregthatcher.com/Mathematics/GaussJordan.aspx

OMG thanks you so much!

Sure! I can help you solve these equations using matrices.

To solve these equations using matrices, we need to first write the system of equations in matrix form.

Let's define the coefficient matrix A, the variable matrix X, and the constant matrix B as follows:

A = | 2 -3 -2 |
| 1/4 -2/5 3/4 |
| -2 1.3 -3 |

X = | x |
| y |
| z |

B = | 4 |
| -1/3 |
| 5 |

So, the matrix equation is given by AX = B.

To solve for X, we need to find the inverse of matrix A. The inverse of a matrix A is denoted as A^(-1).

Now, let's calculate the inverse of matrix A by using the Gauss-Jordan elimination method or any other method you are comfortable with.

After calculating the inverse of matrix A, denoted as A^(-1), we can then find X by multiplying A^(-1) with B on both sides of the equation.

X = A^(-1) * B

Finally, plug in the numerical values for matrices A and B and perform the required matrix calculations to find the values of x, y, and z.

I hope this explanation helps you solve the given system of equations using matrices. If you have any further questions, feel free to ask!