Matrix Times Vector

A weighted recipe of the columns.

12 problems · about 22 minutes · N-VM.C.11, N-VM.C.12

NameDate

Figure — use these to answer the problems

The product is shown beside the matrix. Set the vector to ⟨1, 0⟩ and the answer becomes the first column exactly.

row 1, column 12

row 1, column 21

row 2, column 13

row 2, column 24

vector, first entry1

vector, second entry0

Figure 1

Straightforward practice. Get the method working first.

5 problems

A has columns ⟨2, 1⟩ and ⟨0, 3⟩. What is the first entry of A times ⟨4, 5⟩?
Answer
2
What is Ax, viewed the useful way?
- A linear combination of the columns of A, weighted by the entries of x.
- The sum of every entry in A and x.
A has columns ⟨2, 0⟩ and ⟨0, 5⟩. What is the first entry of A times ⟨3, 1⟩?
Answer
The same A. What is the second entry of A times ⟨3, 1⟩?
Answer
A times ⟨0, 1⟩ gives which column of A? Enter 1 or 2.
Answer

The same ideas with more to keep track of.

3 problems

A times the zero vector. What is every entry of the result?
Answer
A 2 by 5 matrix times a suitable vector. How many entries does the answer have?
Answer
Row 1 of A is [4, 2] and x = ⟨3, 1⟩. What is the first entry of Ax?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Match each product to its result.
Draw a line from each item on the left to its match on the right.
- A times ⟨1, 0⟩
- A times ⟨0, 1⟩
- A times ⟨0, 0⟩
- The first column of A
- The second column of A
- The zero vector
A has columns ⟨1, 1⟩ and ⟨1, 1⟩. What is the second entry of A times ⟨2, 3⟩?
Answer
The First Column
A has columns ⟨3, 7⟩ and ⟨1, 2⟩. What is the first entry of A times ⟨1, 0⟩?
Answer
The Size
A 3 by 4 matrix times a vector. How many entries must that vector have?
Answer