Finishing up Chapter 5

Will this code enter the if statement? G=[30,55,10] if G<50 count = count +1; disp(G); end The code inside the if statement is not executed, because the comparison is not true!!

For Loops for index = [matrix] commands to be executed end The loop starts with a for statement, and ends with the word end. The first line in the loop defines the number of times the loops will repeat, using an index number. The loop is executed once for each element of the index matrix identified in the first line The index of a for loop must be a variable.

Here’s a simple example In this case k is the index – the loop is repeated once for each value of k the index can be defined using any of the techniques we’ve learned

While Loops while criterion commands to be executed end While loops are very similar to for loops. The big difference is the way MATLAB decides how many times to repeat the loop. While loops continue until some criterion is met.

This loop creates the matrix a, one element at a time

Improving the Efficiency of Loops In general, using a for loop (or a while loop) is less efficient in MATLAB than using array operations.

Chapter 6: Mathematical Insight and Engineering

What is A’? >> A = [1, 2, 3; 4, 3, 6]; >> A’ A B C D This is the transpose= the rows and columns are flipped

What is C? >> A = [1, 2, 3]; >> B = [4, 2, 1]; >> C=dot(A,B) A B. 11 C D Dot product = sum of the elements in vector A multiplied by same elements in vector B

What is C? >> A = [1, 2, 3; 3, 2, 1]; >> B = [1, 1; 1, 1; 1, 1]; >> C=A*B A B. 11 C D Matrix multiplication= dot product of each row of A with each column of B

Matrix Inverse MATLAB offers two approaches The matrix inverse function  inv(A) Raising a matrix to the -1 power  A -1

A matrix times its inverse is the identity matrix Equivalent approaches to finding the inverse of a matrix

Not all matrices have an inverse Called Singular Ill-conditioned matrices Attempting to take the inverse of a singular matrix results in an error statement

Determinants Related to the matrix inverse If the determinant is equal to 0, the matrix does not have an inverse The MATLAB function to find a determinant is det(A)

What is B? >> A = [1, 2; 3, 2]; >> B=det(A) A.0B. 4 C. -4 D. 8 Don’t have to know the mathematics of the determinent

Solutions to Systems of Linear Equations

Using Matrix Nomenclature and AX=B

We can solve this problem using the matrix inverse approach This approach is easy to understand, but its not the more efficient computationally

Matrix left division uses Gaussian elimination, which is much more efficient, and less prone to round-off error

What is C? >> A = [1, 0; 0, 1]; >> B = [5; 2] >> C = inv(A)*B A.1 1B. 5 2 C. 5 1 D.5 2 Don’t have to know the mathematics of the determinent

In-class assignment – Chapter 6 problems 3, 7, 8, and 10