EMT 202 Engineering Math 2 Quiz 2

Our second quiz will be on Monday, June 22, 2015. Please review the following matrix methods in solving unknowns for sets of linear equations.

  1. Cramer’s rule. This method makes use of the determinants in finding the solutions. Using the minor’s method, determinants can be solved easier. Very important for the minor’s method is the use of the conventional signs. Any rows or columns can be utilized as long as conventional signs are observed. Then use the formulas for the unknowns.

2. Gaussian Elimination method. This is the most used among the upper triangular matrix system in solving sets of linear equation. Of course transform first three sets of equation into the augmented matrix form. Any legitimate row operations can be used to achieve the required upper triangular matrix. Then, finally, back substitution will solve the unknowns.

3. Gauss Jordan. This method is just a continuation from Gaussian elimination by making the diagonal line into 1’s and zeros upper and lower matrices. Row operations are used to attain the form. Since the diagonal elements are 1’s, unknowns can be solved readily.

4. Inverse Method. This is derived from the AX= b equation. Of course, A is a coefficient matrix, X represents the unknowns, and b, are the constants. Transforming such equation into X = A -1b, may solve the equation where A -1 is the inverse of A.

 

Try the sets of linear equations below. Solve the following sets of equations by

a) Cramer’s rule b) Gaussian elimination

c) Gauss Jordan method d) Inverse method

                       2x – y + 2z       = 7

                        x + 3y -3z        = 10   

                        3x – 2y + 3z    = 5

Answers:        x = 1                y= 11               z= 8

  1. Victor E. Odarve, BSME/MEP-ME, MAED, EDD

Mayana, Jagna, Bohol, Philippines, Southeast Asia

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MULTIPLICATION OF MATRICES-MS EXCEL

Addition and subtraction of matrices do not offer much difficulty to the student. Basically the operation follows the usual arithmetic operation. But multiplication of matrices is a different matter. It is quite difficult as some rules are to be followed. The difficulty of operation increases as the size of the matrices to be multiplied also increases.

MS Excel becomes a valuable tool in obtaining a solution for matrices multiplication. The program saves time and effort. For purpose of illustration, open the MS Excel and solve the following matrices;

EXAMPLE: Find the product of matrix AB.
If matrix A= 4           2         3
1            1         2
2           1          3
and matrix B =    2         4
1           0

1           2

Find AB.

Solution:
Highlight vacant cells for the product. The product
is a 3×2 size. Then move the cursor to the formula bar and put = sign.
Then at Formula heading, browse for function MMULT. Dialogue box
appears. On array 1, highlight data of matrix A. On array 2, highlight
data of matrix B. Then press F2. Then press Ctrl + Shift + Enter
simultaneously. Answer appears at the space provided for the product, as follows;

13          22
5           8
8           14

Below is a dialogue box as shown in the spreadsheet.

Dialogue box where you enter the matrix data.

Dialogue box where you enter the matrix data.