Can somebody show I how to rewrite these four equations as matrix equation to enter into a calculator Ti84. I think I support to seperate something first into two different parts before input into a calculator but
don't know what to seperate nor how many row or column.
eq1: NAB+0.1NABcos(15)+0.1=0
eq2: NABcos(15)-0.1NABsin(15)+NC=0
eq3: -3000+.2NB+0.2NABcos(15)+NABsin(15)-ND=0
eq4: 0.2NAB+NABcos(15)+0.2NB=0
To rewrite these four equations as a matrix equation, we can follow these steps:
Step 1: Identify the variables and constants in the equations.
From the given equations, we can identify the following variables: NAB, NC, NB, and ND. The constants are as follows: 0.1, 0.2, 0.1*cos(15), 0.1*sin(15), 0.2*cos(15), 0.2*sin(15), -3000.
Step 2: Create a matrix for the coefficients of the variables.
To create a matrix for the coefficients of the variables, we need to separate the equations into their individual terms.
For eq1: NAB + 0.1*NAB*cos(15) + 0.1 = 0
Separate terms: NAB, 0.1*NAB*cos(15), 0.1
For eq2: NAB*cos(15) - 0.1*NAB*sin(15) + NC = 0
Separate terms: NAB*cos(15), -0.1*NAB*sin(15), NC
For eq3: -3000 + 0.2*NB + 0.2*NAB*cos(15) + NAB*sin(15) - ND = 0
Separate terms: 0.2*NB, 0.2*NAB*cos(15), NAB*sin(15), -3000, -ND
For eq4: 0.2*NAB + NAB*cos(15) + 0.2*NB = 0
Separate terms: 0.2*NAB, NAB*cos(15), 0.2*NB
Step 3: Write the matrix equation.
Based on the separated terms, we can rewrite the equations in matrix form as:
⎡ 1 0.1*cos(15) 0 0 ⎤ ⎡ NAB ⎤ ⎡ -0.1 ⎤
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎢ cos(15) -0.1*sin(15) 0 1 ⎥ ⎢ NC ⎥ ⎢ 0 ⎥
⎢ ⎥ * ⎢ ⎥ = ⎢ ⎥
⎢ 0 0.2*cos(15) sin(15) 1 ⎥ ⎢ NB ⎥ ⎢ 3000 ⎥
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣ 0 cos(15) 0 0.2⎦ ⎣ ND ⎦ ⎣ 0 ⎦
This is a matrix equation where the coefficient matrix on the left multiplies the variable matrix, and the constant matrix is on the right-hand side.
Step 4: Enter the matrix into a Ti-84 calculator.
To enter this matrix equation into a Ti-84 calculator, follow these steps:
1. Press the [MODE] button.
2. Use the arrow keys to navigate to the "Matrix" option and press [ENTER].
3. Select "Edit" and press [ENTER].
4. Choose a matrix letter (e.g., [A]) and set the dimensions according to the number of rows and columns in the matrix equation.
5. Enter the coefficients of the matrix equation into the matrix.
6. Repeat steps 4 and 5 for each matrix in the equation (variables and constants).
7. Press the [2ND] button, then [MATRIX], and choose the "Math" option.
8. Select "rref(" for row-reducing the matrix equation.
9. Enter the name of the matrix equation that you have created, and close the parenthesis.
10. Press [ENTER] to calculate the row-reduced form of the matrix equation.
The calculator will display the solution to the matrix equation in row-reduced echelon form.