Matrices

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I am attaching the questions to the email. I am looking for the correct answers for all the questions. Please send me the answers by 2 PM CST.

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 *i*^{th} row and in the *j*^{th} 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 *i*^{th} row and in the *j*^{th} 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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