Matrices + Vectors

Question 1

How do you multiply matrices?

Answer 1

Question 2

How do you find the inverse of a 2x2 matrix?

Answer 2

Question 3

What is the feature of the inverse of a matrix?

Answer 3

Question 4

How do you find the inverse of a matrix?

Answer 4

Question 5

How do you find adj(A)?

Answer 5

Question 6

How do you find the unit vector?

Answer 6

Question 7

How do you find the normal of a plane using two unit vectors?

Answer 7

Question 8

What is the cross product rule?

Answer 8

Question 9

What is the equation of a traingle?

Answer 9

Question 10

How do you multiply vectors?

Answer 10

Question 11

How do you calculate eigenvalues?

Answer 11

Question 12

How do you calculate eigenvectors?

Answer 12

Question 13

How do you find the intersection of a point and a line?

Answer 13

Question 14

How do you find the smallest distance between a point and a line?

Answer 14

Question 15

How do you find the intersection of two lines?

Answer 15

Question 16

How do you find the distance between two lines?

Answer 16

Equation given in book.

Remember a x b does not equal a · b!

Work a x b out first and then just insert this value into the equation. You can also find |a x b| from this which is again inserted into equation!

Question 17

How do you find the angle between two lines?

Answer 17

Question 18

How do you find the distance between a point and a plane?

Answer 18

Question 19

How do you find the angle between a point and a plane?

Answer 19

Question 20

How do you find the intersection of two planes?

Answer 20

Question 21

How do you find the distance between two planes?

Answer 21

Question 22

How do you find the angle between two planes?

Answer 22

Question 23

How do you find the transformation matrix for image points?

Answer 23

Question 24

How do you find the image of a point?

Answer 24

Question 25

Hows do you find the image of a transformed plane?

Answer 25

Question 26

How do you set up simultaneous equations using matrices and vectors?

Answer 26

Question 27

How do you perform Gaussian elimination to solve simultaneous equations?

Answer 27

Question 28

What is the quadratic formula?

Answer 28

Question 29

How do you complete force problems?

Answer 29

1. Calculate the unit direction vectors in which you need to find the force.
2. Calculate the force direction unit vector.
3. Calculate the force vector by multiplying the unit vector by the magnitude of force.
4. Use the dot product between the force vector and each unit direction vector in order to find the force in that direction.

Question 30

How to model mass-spring systems

Answer 30

Question 31

How do you find inclined asymptotes?

Answer 31

• If numerator has higher power then denominator:

Divide numerator by denominator to find equation for asymptote.

• If denominator has higher power then numerator:

There is a horizontal asymptote at y=0.

• If numerator and denominator both have same maximum power:

Take the coefficients of these maximum powers and divide.

3x² + x = 3 = 3

x² +1 1

Question 32

​How do you find the volume of revolution of a 3D shape?

Answer 32

If the curve of the shape is constant the throughout (such as a bowl) you can ignore the one plane and set to zero (for example y = 0.

You can then use the equations to solve as normal.

Watch for upper and lower values.

If symmetrical, pick one side of the axis as this will revolve 360 degrees around axis and give no overlap.