Matrices & Systems — Drills
Matrices & Systems has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 9 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Mean — Two kinds of centre: the balance point, and the middle value.
- Coefficient — The number multiplying a variable — the 3 in 3n.
- System — Two or more equations that must hold at the same time.
- Parallel — Same slope, different intercept.
- Diagonal — A segment joining two non-adjacent vertices.
- Matrix — A rectangular array of numbers, described by its rows then columns.
- Dimensions — Rows × columns. A 2 × 3 matrix has two rows and three columns.
- Identity matrix — The square matrix with ones down the diagonal; it leaves everything unchanged.
- Determinant — A single number computed from a square matrix; zero means it has no inverse.
Det
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the determinant of [-352-4].
Worked answer
2
(-3)(-4) - (5)(2)
= 12 - 10 = 2
Problem 2
Find the determinant of [13-58].
Worked answer
23
(1)(8) - (3)(-5)
= 8 - -15 = 23
Shape
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A 4 × 4 matrix multiplies an 4 × 5 matrix. Give the dimensions of the result, as rows x columns.
Worked answer
4x5
Inside numbers are both 4, so it works
Result is 4 × 5
Problem 2
A 5 × 4 matrix multiplies an 4 × 3 matrix. Give the dimensions of the result, as rows x columns.
Worked answer
5x3
Inside numbers are both 4, so it works
Result is 5 × 3
Multiplying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the top entry of [3320][74].
Worked answer
33
3(7) + 3(4) = 33
Problem 2
Find the bottom entry of [5215][42].
Worked answer
14
1(4) + 5(2) = 14
Finding the constant
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find k so that [5522] has no inverse.
Worked answer
5
2k - 10 = 0
k = 5
Problem 2
Find k so that [36982] has no inverse.
Worked answer
36
2k - 72 = 0
k = 36
System
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For the system 1x+4y=7, 3x+12y=1, find the determinant of the coefficient matrix.
Worked answer
0
(1)(12) - (4)(3) = 0
So there is no unique solution
Problem 2
For the system 3x+3y=7, 6x+6y=1, find the determinant of the coefficient matrix.
Worked answer
0
(3)(6) - (3)(6) = 0
So there is no unique solution