Matrices
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SAMPLE ANSWER
Matrices
Question 1: Compute the products
- Graphical drawings of the column vectors
Question 3: Find two inner products and a matrix product
Two inner products (-14, -14)
Matrix product =
Two inner products (-14, 15)
Matrix product =
Two inner products (-14, 15)
Matrix product =
Question 5: Solution for x
Question 6: Solving a 2 by 2 matrices
Solution: since indicates the entry in A which is in the ith row and in the jth column, we see that:
Likewise
Therefore,
Also,
Question 10: True or false statements
- True
- True
- True
- False
Question 24:
Question 30:
Gaussian Elimination
Question1:
Question 3:
2x – 3 y = 3 2x – 3 y = 3 x = 3 Subtract 2 x row 1 from row 2
y + z = 1 gives y + z = 1 and y = 1 Subtract 1 x row 1 from row 3
2y – 3z = 2 -5z = 0 z = 0 Subtract 2 x row 2 from row 3
Question 10:
Question 11:
Question 17:
Question 28:
- True
- False
- True
The Geometry of Linear Equations
Question 1:
The lines intersect at (x, y) = (3, 1). Then 3(column 1) + 1(column 2) = (4, 4).
Question 9:
Column 3 = 2(column 2) – column 1. Ifb = (0, 0, 0), then (u, v, w) = (c, -2c, c)
Question 13:
The row picture has two lines meeting at (4, 2). The column picture has 4(1, 1) +
2(-2, 1) = 4(column 1) + 2(column 2) = right-hand side (0, 6).
Matrices
Question 1: Compute the products
- Graphical drawings of the column vectors
Question 3: Find two inner products and a matrix product
Two inner products (-14, -14)
Matrix product
Two inner products (-14, 15)
Matrix product =
Two inner products (-14, 15)
Matrix product =
Question 5: Solution for x
Question 6: Solving a 2 by 2 matrices
Solution: since indicates the entry in A which is in the ith row and in the jth column, we see that:
Likewise
Therefore,
Also,
Question 10: True or false statements
- True
- True
- True
- False
Question 24:
Question 30:
Gaussian Elimination
Question1:
Question 3:
2x – 3 y = 3 2x – 3 y = 3 x = 3 Subtract 2 x row 1 from row 2
y + z = 1 gives y + z = 1 and y = 1 Subtract 1 x row 1 from row 3
2y – 3z = 2 -5z = 0 z = 0 Subtract 2 x row 2 from row 3
Question 10:
Question 11:
Question 17:
Question 28:
- True
- False
- True
The Geometry of Linear Equations
Question 1:
The lines intersect at (x, y) = (3, 1). Then 3(column 1) + 1(column 2) = (4, 4).
Question 9:
Column 3 = 2(column 2) – column 1. Ifb = (0, 0, 0), then (u, v, w) = (c, -2c, c)
Question 13:
The row picture has two lines meeting at (4, 2). The column picture has 4(1, 1) +
2(-2, 1) = 4(column 1) + 2(column 2) = right-hand side (0, 6).
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