part 2: Matrices
Section 1: Entering Matrices into a calculator
To insert matrices into a calculator, press second, matrix and then press the right arrow key twice to go over to edit. Here you can fill in matrix A-J. press whichever one you want to fill in and then change the dimensions at the top right by just typing in the right dimensions and pressing enter. The first number (1x1) will be your rows and your second number (1x1) will be your columns. After you’ve filled in your dimensions you can press the down arrow and start filling in your numbers in the matrix. Just arrow over until you’re on the number you want to change and then type in the right number and press enter. Do the same for every spot in the matrix and then press enter.
Section 2: Adding and subtracting matrices
Matrices have to be the same dimensions to add or subtract. When adding or subtracting two matrices, press second, matrix and then press the right key twice to go over to edit. Fill in the correct matrices with the correct information. (refer to section 1) then go back over to names and press whichever matrix you want first. It will then show up on your home screen. Press the add or subtract symbol and then go back to second, matrix, names and press the second matrix you want. Press enter and it will give you your answer. If you try to add or subtract two matrices that have different dimensions, it will come up with an error screen.
Section 3: Multiplying matrices
To multiply matrices, the two inner dimensions have to correlate ((2x1) and (1x2)). After you enter the matrix information (refer to section 1) press second, matrix and names and choose the matrix you want by pressing enter. Then press the multiplication key and go back and choose the second matrix you want, the same way you chose the first. Then press enter. This will give you the answer.
Section 4: Scalar matrix multiplying
Scalar multiplication with matrices is where there is a number outside of the matrix, multiplying the whole matrix by it. In this case, type in the first number that is being multiplied by the whole matrix, and then fill in your matrix information (refer to section 1). Press second, matrix and names and then choose the matrix you want to multiply by pressing enter. Press enter again and your answer will appear.
Section 5: finding the inverse of a matrix
To find the inverse of a matrix, first type in the correct matrix information (refer to section 1). Then press Second, Matrix, Names and choose the matrix you want by pressing enter. Press the x^(-1) key and then enter. Your answer will show up on the screen. If the answer is a decimal and you can’t see it all, press the Math key and arrow down to Frac (fraction) and press enter twice. This should turn you matrix into a fraction and allow you to see it all on the screen.
Section 6: solving Systems of equations with matrices
Example: 8x+12y=364 and 1x+4y=93
On Paper: Take the numbers multiplying x and y (8, 12, 1, 4) from your equations and create a 2x2 matrix by putting the first equation's numbers on the top two spaces of the matrix and the second equation's on the bottom two spaces of the equation. This matrix will be called matrix A. Then create a 2x1 matrix with x on top and y on bottom, and write down matrix A being multiplied by this matrix. Take the two right sides of the equations and make another 2x1 matrix with the first equation's on top and the second's on bottom. This will be called matrix B. Make this the right side of your matrix equation. Multiply both sides of the equation by the inverse of A ([A]^-1). This cancels out matrix A, so the matrix containing x and y is on one side of the equation and the inverse of A multiplied by matrix B is on the other side. It is now ready to be inputted into your calculator.
On Calculator: Input matrix A and B into the calculator (refer to section 1). Select matrix A by pressing second, matrix, names and then arrowing down to matrix A and pressing enter. Then press the x^(-1) key. Press the multiplication button and then choose matrix B the same way matrix A was chosen, and press enter. Your answer should display on the screen.
On Paper: Take the numbers multiplying x and y (8, 12, 1, 4) from your equations and create a 2x2 matrix by putting the first equation's numbers on the top two spaces of the matrix and the second equation's on the bottom two spaces of the equation. This matrix will be called matrix A. Then create a 2x1 matrix with x on top and y on bottom, and write down matrix A being multiplied by this matrix. Take the two right sides of the equations and make another 2x1 matrix with the first equation's on top and the second's on bottom. This will be called matrix B. Make this the right side of your matrix equation. Multiply both sides of the equation by the inverse of A ([A]^-1). This cancels out matrix A, so the matrix containing x and y is on one side of the equation and the inverse of A multiplied by matrix B is on the other side. It is now ready to be inputted into your calculator.
On Calculator: Input matrix A and B into the calculator (refer to section 1). Select matrix A by pressing second, matrix, names and then arrowing down to matrix A and pressing enter. Then press the x^(-1) key. Press the multiplication button and then choose matrix B the same way matrix A was chosen, and press enter. Your answer should display on the screen.
Section 7: Solving Word problems with matrices
Example: Ming and Carlos are selling cookies for a school fundraiser. Customers can buy packages of chocolate chip cookies and packages of gingerbread cookies. Ming sold 8 packages of chocolate chip cookies and 12 packages of gingerbread cookies for a total of $364. Carlos sold 1 package of chocolate chip cookies and 4 packages of gingerbread cookies for a total of $93. Find the cost each of one package of chocolate chip cookies and one package of gingerbread cookie.
On Paper: First, equations need to be made. Think of the cost of chocolate chip cookies as x and the cost of gingerbread cookies as y. Take the amount of each sold and multiply it by the cost of each (8x+12y and 1x+4y). Then equal that to the amount of money made (364 and 93). Do this for both situations.
On Calculator: From here, the problem is the same as solving systems of equations as seen in section 6. (refer to section 6) When you have found your answer, convert x back to the price of chocolate chip cookies ($17) and y back to the price of gingerbread cookies ($19).
On Paper: First, equations need to be made. Think of the cost of chocolate chip cookies as x and the cost of gingerbread cookies as y. Take the amount of each sold and multiply it by the cost of each (8x+12y and 1x+4y). Then equal that to the amount of money made (364 and 93). Do this for both situations.
On Calculator: From here, the problem is the same as solving systems of equations as seen in section 6. (refer to section 6) When you have found your answer, convert x back to the price of chocolate chip cookies ($17) and y back to the price of gingerbread cookies ($19).
SECTION 8: DETERMINING DEFINED AND UNDEFINED MATRICES
Defined matrices are matrices that can be solved. If you end up with an answer to a matrix problem, the matrix is defined. If you try to solve a matrix problem on you calculator and you get an error screen, the matrix is undefined and cannot be solved. This is usually due to matrix dimensions not matching up.