3x3 matrices IB SL/HL maths

3x3 Matrices By the end of this lesson you will be able to: find the determinant of a 3x3 matrix without a GDC. find inverses and determinant of 3x3 matrices using a GDC. solve simultaneous equations using in 3 or more unknowns using a GDC.

Determinant of a 3x3 matrix without a GDC Sometimes this is better seen and remembered by using a diagram: - + Highlight a, then cancel the numbers in a ’s column and row. Find the determinant of the 2x2 matrix remaining. Continue for b and c. Remember to subtract b.

Now some practise… Find the determinants of each matrix.

Using your GDC to get the determinant. The TI 1.Enter a 3x3 matrix. Go to the Matrix function by 2nd x -1. Tab across to Edit, and ENTER. Choose the dimensions: 3x3, and enter in your matrix. 2. Quit when you have entered your matrix. Go back into the Matrix function, and tab across to MATH, choose option 1; now go back to Matrix and choose A. The Casio 1.From the main menu choose Matrix option, choose a matrix and set it’s dimensions. Enter the matrix. 2.Go back to the main menu and go into Run. 3.Choose OPTN, F2, F3 ( Det ), then F1 ( Mat ), ALPHA, and choose the matrix you entered.

Using your GDC to get the inverse of a 3x3 matrix. The TI 1.Enter the matrix as before. 2.Go into the Matrix menu and select matrix from the first menu. 3.Now select the x -1 and ENTER. 4.To get the numbers as fractions you must now enter ANS FRAC (from the MATH menu). The Casio 1.Enter the matrix as before. 2.Go into the Run menu, and choose OPTN, followed by F2 and F1, ALPHA and choose the matrix. 3.When the matrix is on the screen put it to the power of negative 1. Ensure that you use SHIFT ) and not ^ button.

Solving a simultaneous equation with 3 unknowns. Solve these simultaneous equations: Look at the simultaneous equations and it could be written as: This can be written as: Remove the A by multiplying both sides by A -1. Now on your GDC multiply the two matrices to give the values: x =4, y =-1, z =2

Now solve these equations: