Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2001 / Paper 1 / 7 / a

Table of contents
- i a
  - Solution i
- ii a
  - Solution ii
- iii a
  - Solution iii
- iv a
  - Solution iv

i

Solution

Subtract corresponding entries in the two matrices:

(2 - 6 - 10 - 3 15 - 6) .

Both matrices have shape

2 \times 3

, so this subtraction is defined.

ii

Solution

Using row-column matrix multiplication, the second row of the first matrix is

(1, 6)

. Therefore

(3176) (2040) = (62124) .

iii

Solution

The row-column product is the dot product

4 \cdot 6 + 8 \cdot 3 + 1 \cdot 0

48

. Its shape is

1 \times 1

.

iv

Solution

The first matrix product gives the column

(37, 37, 37)^{T}

. Its product with the final row is an outer product, not a scalar:

373737 (- 2 02) = - 74 - 74 - 74 000747474 .

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