Can somebody show I how to use matrices to solve the following. I want to solve for Tab first. I wiill ask 9n other part later. It given Tad =1200.
.285Tab-.428Tac=0
-.428Tab-.285Tac+.384Tad=0
-0.857Tab-.857Tac+.923Tad=0
Anonymous
15 hours ago
No need for matrices, since all these linear combinations just add to zero.
If AX = 0 (all matrices) then X=0
Or, using Cramer's rule, since all the numerators have a zero column, they are all zero.
👤
oobleck
11 hours ago
I don't know what that is . I plug in Tad=1200 and I get
eq1) 285Tab-.428Tac=0
eq2) -.428Tab-.285Tac+460.8=0
eq3) -0.857Tab-.857Tac+1107.6=0
Now how do I use eq1 and eq2 to to solve for Tab and Tac?
Google Gauss Jordan calculator
You know the answer already, but the calculator will get you through the steps.
To solve for Tab and Tac, we can rearrange the given equations and then use matrix methods.
First, let's rewrite the equations using the given values of Tad = 1200:
eq1: 285Tab - 0.428Tac = 0
eq2: -0.428Tab - 0.285Tac + 460.8 = 0
eq3: -0.857Tab - 0.857Tac + 1107.6 = 0
Now, we can set up a matrix equation using the coefficients of Tab and Tac. The matrix equation will be in the form AX = B, where:
A = coefficients matrix
X = unknowns matrix (Tab, Tac)
B = constant matrix (0, -460.8, -1107.6)
The coefficients matrix A is obtained from the coefficients of Tab and Tac in the equations:
A = | 285 -0.428 |
| -0.428 -0.285 |
| -0.857 -0.857 |
The unknowns matrix X is:
X = | Tab |
| Tac |
And the constant matrix B is:
B = | 0 |
| -460.8 |
| -1107.6 |
To solve for X, we can use matrix algebra. We need to find the inverse of matrix A:
A^-1 * A * X = A^-1 * B
To find the inverse of A, we can use any method like Gaussian elimination or matrix inverse formulas.
Once you have the inverse of A, multiply both sides of the equation by A^-1:
A^-1 * (A * X) = A^-1 * B
This simplifies to:
X = A^-1 * B
Finally, multiply the inverse of A with B to obtain the values of Tab and Tac.
Please note that the values of Tab and Tac will depend on the actual values of coefficients in the equations.