Casio fx-CG50 User manual

Matrices and vectors on the fx-CG50
Learning objective
How to perform matrix and vector calculations.
How to save matrices and vectors.
This worksheet accompanies the video Matrices and Vectors-Calculations.
We suggest you watch it first.
How to use the quick method for matrix calculations
Press pand choose Run-Matrix.
Ignore the MAT/VCT menu for now and choose MATH (r).
From here, choose MAT/VCT (q) to find the quick menu for matrices which runs to two screens.
To evaluate
3 2 0 1
1 4 1 0
  
  
−
  
input it exactly as you write it, choosing the 2x2 template (q) and scrolling
across rather than using lto complete the matrix. Then, press lto perform the calculation.
To find the determinant of the answer, you will need the determinant function which is found in the
optional Matrix menu.
Press iand choose MAT/VCT (w) followed by Det (e) from the menu.
If you try to just use Ans here, an error message appears –you need to choose Mat (q) and use Ans
(L-n).

- 2 -
Using the Matrix menu for matrices of other sizes
To find the image of the shape made from the four points (1, 0), (1, 5), (3, 4), (1, 3) under the rotation
represented by the matrix
cos60 sin 60
sin 60 cos60
 − 




you need the matrix product
cos60 sin 60 1 1 3 1
sin 60 cos60 0 5 4 3
 − 
  
  

  
.
You can define these matrices as matrix A and matrix B and then multiply them.
Press dtwice to leave the current menus, then choose MAT/VCT (e) and press lto select Mat A.
Input the dimensions 2x2and enter the coefficients. Input the expression (e.g.
cos60
). There is no need
to work them out first, the values will appear as you enter them using l. Make sure that your calculator
is set to degrees.
Press dto enter matrix B in Mat B. This time, select 2x4and press lto enter the values.
These matrices can now be used as many times as you wish. Press dtwice to return to the main screen.
The matrix for calculation can be chosen either by press Mat (L-2), or by pressing iand choose
MAT/VCT, then choose MAT. Use A(a-f) and B(a-g) for MatAxMatB. The multiplication sign
is optional but good practice. Press l.
The answer matrix is too big to fit on the screen, so scroll up to the answer and to the right to see the rest
of the matrix. Notice that the values are given in surd form here.

- 3 -
Using Run-Matrix for vector calculations
Press dtwice to return to the first menu and choose MAT/VCT.
Choose M⇔V(u) to access the vector menu.
Enter the vectors Vct A =( 3
−1
2)Vct B =( 2
0
−3)by selecting each in turn, setting the size of the vector
and entering the values.
Press dto return to the list of vectors. If you make a mistake, you can delete the vector from the first
screen.
Press dtwice to return to the Run-Matrix menu and press iand choose MAT/VCT.
Then choose further menu (u) twice to find the third set of options.
For scalar product (dot product) choose DotP( (w) first, then input the two vectors using qand a,
and ,to separate them.
Pressing lwill give the value zero in this case.
Vector product (cross product) is input in the same way.

- 4 -
Taking it further - saving vectors and matrices
Turning the calculator off will not lose the vectors and matrices you have named. Resetting the calculator
will clear them.
Vectors and matrices, like lists in Statistics mode, can be saved as CSV files in the calculator memory to be
used again. Once saved, resetting the calculator will not delete them.
From the list of matrices, choose CSV (r) followed by SAVE-AS (press w).
Scroll to the folder you wish to save into and press qto save.
You can rename the matrix, if you wish––you must press afor each letter you use––and scroll to the
right of a letter that you wish to delete before using the okey.
To retrieve your matrix, choose MAT/VCT (e) from the Run-Matrix menu.
Then choose CSV (r) followed by LOAD (q).
Scroll to return to the folder where you saved your matrix and choose OPEN (q) to open subfolders (if
you have them) and OPEN again to open the file.