2 - week2

Question 1

Property of inverse matrix A-1

Answer 1

Inverse A * Matrix A = Identity matrix

Question 2

There are three types of elementary row operations:

Answer 2

1. Swapping two rows,
2. Multiplying a row by a nonzero number,
3. Adding a multiply of one row to another row.

Question 3

More on inverse matrix

Answer 3

The inverse of a number is its reciprocal.

The matrix must be square (same number of rows and columns).

The determinant of the matrix must not be zero. (eg. ad-bc = 0)

A square matrix that has an inverse is called invertible or non-singular. A matrix that does not have an inverse is called singular.

A matrix does not have to have an inverse, but if it does, the inverse is unique.

An inverse of a number is denoted with a −1 superscript.

Question 4

exponentiating a matrix

Answer 4

Example from class:

(A**5)**3 = A**15

Question 5

Transpose

Answer 5

Question 6

Vectors

Answer 6

Vectors represent a solution or result or something like that

Question 7

Row operations

Answer 7

Question 8

What is Echelon Form?

Row echelon form.

Reduced row echelon form

Answer 8

Row echelon form:

Everything below the “1’s” must be 0 in each column

Reduced row echelon form:

Everything above and below the “1’s” must be 0 in each column

Question 9

Class Eqation 1

Question 10

You have the row echelon form when?

Answer 10

When you have all 1’s in the diagonal and zeros below it.
Whatever is above dosnt matter

Question 11

Determinant of a Matrix

Answer 11

The symbol for determinant is two vertical lines either side.

|A| means the determinant of the matrix A

(Exactly the same symbol as absolute value.)

The determinant of a 2x2 matrix is:

|A| = ad − bc

Question 12

4 steps of the algorithm for RREF

Answer 12

1) find the leftmost column that is not all 0’s
2) get the non-zero entry at the top of this column

3) make this entry 1: multiply the first row by a suitable number or interchange the two
4) Add suitable multiples of the top row to rows below so that all entries below the leading one become zero

Question 13

Basic and Free variables

Answer 13

Basic Variables = Pivot rows when 1 is the first non zero number

Free Variables = q-p = nr. of free varables

(When you have free variables there are infinite number of solutions)

Question 14

Writing solutions in vector form

Answer 14

1. put them as eqations
2. order them in vetor
3. show the constant values in vector form
4. • s (show the s “values”)
5. • t (show the t “values”)

Question 15

Ligningsopgave fra bog

Answer 15