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Further Maths > Matrices > Flashcards

Matrices Flashcards

1
Q

What is the order of a matrix?

A

It is rows x columns.

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2
Q

What are square matrices?

A

They are matrices with the same of columns and rows.

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3
Q

What is the 2x2 identity matrix?

A 
It is (10)
       (01)
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4
Q

What is the 2x2 null matrix?

A

(00)

00

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5
Q

What condition must two matrices satisfy to be called equal?

A

They must be completely identical.

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6
Q

When can matrices be added or subtracted?

A

When their order is the same, otherwise they are non conformable for addition.

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7
Q

Difference between matrix addition and subtraction?

A

Addition is associative and commutative, whereas subtraction is neither.

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8
Q

When can u multiply two matrices together?How can you determine the order of the resulting matrix?

A

U can multiply them together if their middle number is the same.The order of the resulting matrix is the two outside number together.

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9
Q

What are the properties of matrix multiplication?

A

It is associative but not commutative.

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10
Q

What does associative and commutative mean?

A

Associative means you can group different numbers together and still get the same result.Commutative means you can change the order in which you carry out the operation and still get the same answer.

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11
Q

What is a rectangular matrix?

A

It is a matrix in which the number of rows are not equal to the number of columns.

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12
Q

What happens when you multiply a matrix by the zero matrix?

A

You result in a zero matrix.

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13
Q

What happens when you multiply a matrix by the identity matrix?

A

You get the same matrix.

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14
Q

What is a symmetric matrix?

A

One that is symmetrical about the leading diagonal.

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15
Q

How can you determine the effect of a 2x2 transformation?

A

See the effect on i and j or do this and use a unit square.

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16
Q

How to calculate shear factor?

A

Distance of imagine from point/distance of original point from x axis.

17
Q

How to do 3d transformations?

A

Consider the effect on i,j and k.

18
Q

How do u apply composite transformations?

A

Multiply the vector by the transformation in reverse order.

19
Q

What is an invariant point?

A

It is a point that maps to itself after a transformation.

20
Q

How to find an invariant line of point?

A

If the two simultaneous equations you get are equal, then that is the equation of the line of invariant points.If they don’t the only invariant point is the origin.

21
Q

What are invariant lines?

A

They are lines where the image of their points after a transformation are on the line.

22
Q

What is the determinant of a matrix?

A

AD-BC

23
Q

How to find the area of a transformation of a matrix?

A

It is just the determinant.

24
Q

What are the cheeky rules for determinants?

A

For square matrices PQ detPQ=det PxQ.
If the determinant of the transformation is 0 the object is mapped to a straight line with zero area.Apart from the null matrix which maps every point to the origin.

25
Q

Whats the determinant of a 2x2 matrix?

A

(1/ad-bc)(d -b)

(-c a)

26
Q

What is a singular and non singular matrix?

A

Singular determinant is zero.Non singular det is not 0.

27
Q

What happens when you multiply a square matrix by its inverse?

A

You get the identity matrix.It is also commutative.

28
Q

What does (AB)^-1 equal for same order matrices?

A

It equals B^-1xA^-1

29
Q

What are the three geometric cases of simulatenous equations?

A
  1. They intersect so one point of intersection
  2. They are parallel so 0 point of intersection
  3. They are coincident so they lie on top of each other and have infinite solutions.
30
Q

What does the determinant of a 3x3 matrix represent?

A

It represents the volume scale factor of the transformation.

31
Q

What is the adjugate of a matrix?

A

It is formed by replacing each element with its cofactor and transposing changing rows into columns and columns into rows.

32
Q

What is a cofactor?

A

It is the minor with the correct sign.

33
Q

How to represent an inverse 3x3 matrix?

A

1/detm x adj m.

Further Maths (20 decks)

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