Column vectors
Across, then up
A column vector has two numbers stacked.
The top number is the movement across (positive is right, negative is left). The bottom number is the movement up or down (positive is up). A vector has a size and a direction, but no fixed starting point.
The vector 3−2 means 3 right and 2 down.
Bold letters such as <b>a</b> name vectors. When you write by hand, underline them.
Working with column vectors
Work row by row. To add, add the top numbers and add the bottom numbers.
To subtract, subtract each row. To multiply by a number, multiply both rows.
- a = (2, 5) and b = (−3, 1), written as columns
- a + b: top 2 + (−3) = −1, bottom 5 + 1 = 6
- 2a − b: top 4 − (−3) = 7, bottom 10 − 1 = 9
The slip to watch: subtracting a negative. 4 − (−3) is 7.
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