[0; x] = [-0.71 0.71; -0.71 -0.71][0.015; 0] + [-0.71 0.71; -0.71 -0.71][cos(y) -sin(y); sin(y) cos(y)][0.035; 0]
I need to solve this matrix for x and y using Excel. Can someone tell me how to do it please?
To solve the given matrix equation [0; x] = [-0.71 0.71; -0.71 -0.71][0.015; 0] + [-0.71 0.71; -0.71 -0.71][cos(y) -sin(y); sin(y) cos(y)][0.035; 0] using Excel, you can follow these steps:
Step 1: Set up the matrix equation
- In Excel, create a table with the following structure:
A | B | C | D
1 0 | x | = | -0.71 0.71 | 0.015
2 -0.71 | -0.71 | + | -0.71 -0.71 | 0
3 -0.71 | | * | cos(y) -sin(y) |
4 0.71 | | | sin(y) cos(y) | 0.035
Step 2: Calculate the results
- In cell B1, enter the formula "=C1*E1 + D1*E2".
- In cell B2, enter the formula "=C2*E1 + D2*E2".
- In cell B3, enter the formula "=C3*G3 + D3*H3".
- In cell B4, enter the formula "=C4*G3 + D4*H3".
Step 3: Solve for x and y
- Now, you can use Excel's Solver tool to find the values of x and y that satisfy the matrix equation.
- In Excel, go to the "Data" tab and click on "Solver" (Note: If you don't see "Solver" in the "Data" tab, you may need to enable it first. Go to "File" > "Options" > "Add-ins", and then check the box next to "Solver Add-in", and click "OK").
- In the Solver window, set the "Set Objective" field to "B1" and choose "Min" or "Max" (it doesn't matter in this case).
- In the "Subject to the Constraints" section, click on "Add" and select the cells B2, B3, and B4, and set the relationship to "Equal to" with a value of 0.
- Click "Solve" and Excel will find the values of x and y that satisfy the equation.
Please note that Solver in Excel uses numerical methods to find approximate solutions. Therefore, the values you obtain may be approximate.