Dimensions — Precalculus, what it means and where it is taught
Rows × columns. A 2 × 3 matrix has two rows and three columns.
Taught in Precalculus.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Matrix — A rectangular array of numbers, described by its rows then columns.
Practise this idea
9 questions in the course bank use Dimensions, in Proportional Reasoning with Scale Drawings, Volume & Surface Area of 3-D Figures, Measurement, Reading Graphs & Estimation, Matrices & Systems, Volume with Fractional Edges. The first 8 are below; the rest are in those units.
Problem 1
If every length is multiplied by 4, the area is multiplied by what?
- 4
- 8
- 16
- 64
Worked answer
16
k2 = 42 = 16
Problem 2
A cube's edge is tripled. Its volume is multiplied by what?
Worked answer
27
k3 = 33 = 27
A 2-cube holds 8; a 6-cube holds 216, which is 27 times as much.
Problem 3
Find the volume of a cube with edge 4 cm.
Worked answer
64
43 = 64 cm3
Problem 4
A cube's edge is doubled. Its volume is multiplied by what?
Worked answer
8
2 × 2 × 2 = 8
A 3-cube holds 27; a 6-cube holds 216, which is 8 times as much.
Problem 5
How many square centimetres are in 1 square metre?
Worked answer
10000
1 m2 is 100 cm × 100 cm
= 10,000 cm2
Problem 6
A pictogram doubles both the height and the width of an icon to show a doubled value. How many times bigger does the icon LOOK?
Worked answer
4
Doubling both dimensions multiplies the area by 2 × 2 = 4
The value doubled but the picture looks four times bigger — a classic distortion.
Problem 7
Give the dimensions of a matrix with 3 rows and 5 columns, in the form rows x columns.
Worked answer
3x5
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Problem 8
A 2 × 3 matrix multiplies a 3 × 4 matrix. Give the dimensions of the result, as rows x columns.
Worked answer
2x4
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