Matrix+Representation


 * 1) Matrices are another way to solve systems of equations other than using substitution or elimination. A matrix is an ordered arrangement of numbers by rows and columns

The matrix below is the matrix representation of an equation with math \left[ \begin{array}{ccc} a_{1,1} & a_{2,1} & a_{3,1}\\ a_{1,2} & a_{2,2} & a_{3,2}\\ a_{1,3} & a_{2,3} & a_{3,3}\\ \end{array} \right] math matrix a equals the coefficients of x, y and z, while b is equal to the constants of the coefficients. This matrix that is shown above is a 3x3 matrix. \vspace{.2in} math \left[ \begin{array}{c} b_{1,1}\\ b_{2,1}\\ b_{3,1}\\ \end{array} \right] math

examples: x+y=2 x+2y=5 The matrix representation: math \left[ \begin{array}{cc} 1 & 1\\ 1 & 2\\ \end{array} \right] math The example that is given is a 2x2 matrix.When you enter this equation in the calculator you would have to: 1. Press the 2nd and then matrix button. 2. You have to press math \rightarrow \rightarrow math When you have done this you would see that your on the edit button. When your there press enter. 3. Press 2 enter 2. 4. Enter the numbers 5. Press the 2nd button and then QUIT. This shows the coefficients of your matrix 6. Repeat steps for matrix B 7. Press 2nd then MATRIX and choose [A] then press ENTER 8. [A] then press X-1, [A] This should show you the constants of your matrix in the calculator. This shows you the constants your your matrix 9. Choose matrix B and press ENTER It should look like this [a]-1[b] Finally, press ENTER. All these steps should give you the final solution of your matrix

3x + 4y=-3z + 5 7x=9y - 2z + 4 6x - 8z=6

This example shown above is a 3x3 matrix. Here are the steps you will have to do to solve the equations.
 * 1) Press the 2nd and then press the matrix button.

2. Next you have to press the math \rightarrow \rightarrow math When you do this you will be at the edit button. When your there press enter. 3. Then press 3 enter 3 4. Enter the numbers given This is how the matrix is supposed to look like 5. Press the 2nd button and then quit 6. Repeat the steps for B matrix B should look like this 7. Press 2nd then matrix and choose [A] and then press enter 8. When [A] is shown press x-1 It should look like this: [A]-1 9. Press 2nd matrix then enter B It should look like this: [A]-1[B] Press enter and it will give you the answer to your final solution

9x= 8y - 8 6x + 3y= z + 9 7x + 8y - 5z= 1 Here now you try and solve this matrix. Good Luck and God Bless Hope you understand what we have presented to you all.