# Week 5 Flashcards

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1
Q

Are vectors matrices?

A

Yes (with N rows and 1 Column)

2
Q

A

3
Q

How to we perform scalar multiplication of matrices?

A

Component-wise multiplication

4
Q

How do we determine dot product?

A
• Component wise multiplication

5
Q

Why is dot product useful?

A

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

6
Q

How to determine norm of vector?

A
7
Q

How to determine orthoganlity?

A
8
Q

How to multiply matrices?

A
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
9
Q

How to determine size of matrix after multiplication?

A

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.

10
Q

Why is the law of associativity useful?

A

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

11
Q

What is Gaussian elimination?

A

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

Operations must be applied simulataneously to each matrix of constants

12
Q

What operations can we conduct for Gaussian elimination?

A

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

13
Q

Should gaussian elimination be done all at once or subsequently?

A

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

Best to do things one at a time