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### 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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