Week 5

Question 1

Are vectors matrices?

Answer 1

Yes (with N rows and 1 Column)

Question 2

How do we add matrices?

Answer 2

Component-wise addition

Question 3

How to we perform scalar multiplication of matrices?

Answer 3

Component-wise multiplication

Question 4

How do we determine dot product?

Answer 4

• Component wise multiplication

- Addition of resulting elements

Question 5

Why is dot product useful?

Answer 5

If dot product equals 0, then matrix/vector is orthogonal

Question 6

How to determine norm of vector?

Question 7

How to determine orthoganlity?

Question 8

How to multiply matrices?

Answer 8

1. Multiply component-wise the first row with the first column, then add up the results
2. Repeat for first row, second column
   …
3. Dot product of row1 and col1 of A and B, respectively
4. Dot product of row1 and col2 of A and B
5. Dot product of row2 and col1
6. Dot product of row 2 and col2
   …

Question 9

How to determine size of matrix after multiplication?

Answer 9

If A is mn and if B is nr
Then AB is m*r

Where m = rows and n = columns for A
and
Where n = rows and r = columns for B

NOTE: This only works if A and B have the same number of columns or rows, respectively.

Question 10

Why is the law of associativity useful?

Answer 10

It doesnt matter which order we evaluate multiplication. Brackets can be anywhere, same result

Question 11

What is Gaussian elimination?

Answer 11

A process using certain operations that DO NOT change the set of solutions.

Operations must be applied simulataneously to each matrix of constants

Question 12

What operations can we conduct for Gaussian elimination?

Answer 12

Type 1. Swap two rows
Type 2. Multiply a row by a NON-ZERO number
Type 3. Add a multiple of one row to another row

Question 13

Should gaussian elimination be done all at once or subsequently?

Answer 13

All done at once can go wrong, can lose info.

Best to do things one at a time