Matrices

Question 1

What does a) AI =? b) BI =?

Answer 1

a) A b) B

Question 2

A(BC) =?

Answer 2

(AB)C

Question 3

How do you find the image of a point (a,b) from transformation M?

Answer 3

Find M[a b]

Question 4

Properties of a linear transformation for vectors a and b

a) T(µa) = ?
b) T(a + b) = ?

Answer 4

a) µT(a)
b) T(a) + T(b)

Question 5

What does it mean when the determinant is negative?

Answer 5

The transformation either is or includes a reflection

Question 6

What does the determinant of 2X2 matrix show?

Answer 6

The area s.f of the enlargement

Question 7

What does the determinant of a 3X3 matrix equal and show?

Answer 7

a.bxc

volume scale factor

Question 8

What does the determinant of the transpose of M =?

Answer 8

The determinant of M

Question 9

Effect on determinant?

a) Adding or substracting any multiple of a row or column to another row or column
b) Interchanging two rows or columns
c) multiplying a row or column by a scalar

Answer 9

a) no effect
b) changes sign of determinant
c) multiplies determinant by that scalar

Question 10

Relationship between IABI and IAI, IBI, IBAI

Answer 10

IABI = IBAI = IAI IBI

Question 11

Transformation represented by inverse of matrix which represents:

a) rotation of ø
b) reflection in a line or plane
c) enlargement s.f k

Answer 11

a) rotation of -ø
b) relection in same line or plane
c) enlargement s.f 1/k

Question 12

A^-1A = ?

Answer 12

AA^-1

= Identity

Question 13

Inverse of a 2X2 matrix

a b

c d

Answer 13

(1/ad - bc ) d -b

-c a

Question 14

Products of inverses rule

Answer 14

(ABC)^-1

= A^-1B^-1C^-1

Question 15

Solving linear equations

when are there no solutions?

Answer 15

Two of the planes are the same

Two of the planes are parallel

or they form a triangular prism

Question 16

When are there an infinite number of solutions?

Answer 16

The three planes form a sheaf

there is a common line

Question 17

How to solve

3X3 matrix x [x y] = [k1 k2] = ?

Answer 17

Find inverse of 3X3 matrix

multiply it by [k1 k2]

Question 18

When is linear independence?

Answer 18

If a vectot is a combination of other vectors, it is linearly dependent on them.

if a(vector 1) + b(vector 2) + c(vector 3) = vector of 0s, they are linearly independent

a b and c are linearly dependent if determinant

a1 b1 c1

a2 b2 c2 = 0

a3 b3 c3