Please solve using excel. See attachment for guidelines and specifications……………………………. and there is an example

linear_equations_hw.pdf

linear_equation_example.pdf

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ETCC 204

Homework #3

Linear Equations

A 10 ft square concrete pad is on a constant plane, but is not level. The corner of the pad is at the

coordinates x = 0 and y = 0, as indicated in the figure below. The station and elevation of three points on

the pad are surveyed. What equation in the form z = Ax By C describes the surface (i.e., what are the

values of A, B and C)? Set up a block to predict the elevation of any point on the pad given the x and y

coordinates using the equation. Have the spreadsheet return the word “Off” if the coordinates entered are

not on the pad. Basically, add an if statement to check whether or not the x’s and y’s you enter are

between 0 and 10 (10 ft wide slab). Note: this check is not exact, because it just checks whether or not

the vertical projection of the plane are within the 10 ft range; if the slab is tilted (as it is in our case), the

actual dimensions of the pad will be longer than 10 ft, but this provides a quick check. Use goal seek to

determine the y coordinate on the plane if the x coordinate is 2 and the z coordinate is 12.88.

Observations:

Point

a

b

c

x (ft)

2.0

4.5

9.0

y (ft)

7.0

2.5

6.0

z (ft above datum)

12.0

10.0

11.5

a

x=0

y=0

c

b

HW Grading Block

Category

Overall given? find format (heading, drawing, equations, calculation explanation, etc.)

Correct matrix setup

Matrix solution (values for A, B, and C) correct, and clearly labeled

Points

Possible

10

5

10

If statement clearly determines if x and y are on plane (correct z value if values are on plane)

10

Total

35

e points on

what are the

entered are

Points

Received

0

B

ETCC 204

Name

Linear Equations

Week 3 – 09/21/2012

Given: Five linear equations with five unknowns.

in equation form:

x1 3×2 – 7×3 4×4 – 2×5 = 2

4×2 – 4×3 6×4 7×5 = 27

2×1 2×2 – 2×3 5×4 – 8×5 = -6

6×1 – 3×2 – 5×3 8×5 = 5

-5×1 – 6×2 5×4 3×5 = -2

These are just text

typed into cells for

display only!

Find: The values of the unknowns (x1, x2, x3, x4, and x5) that balance the equations.

Ax = B

in matrix form:

where:

A

1

3

-7

4

-2

0

4

-4

6

7

2

2

-2

5

-8

6

-3

-5

0

8

-5

-6

0

5

3

Use the =MINVERSE( ) command to invert A:

x

x

b

x1

x2

x3

x4

x5

2

0.019

0.085

0.070

0.085

0.062

0.125

-0.021

0.094

0.127

-0.043

0.099

-0.063

-0.012

0.012

0.019

-0.054

-0.084

-0.017

0.046

-0.001

Only a square matrix may be inverted.

Given the matrices A, x and b, where the dimensions of each are

row x column if you multiply A by x to result in b (i.e., Ax = b) then:

answer has these

x

x

-6

5

-2

x = A-1b

Things to look for in this lecture:

A

=

Use =MMULT( ) to multiply:

A-1

-0.118

0.002

-0.201

-0.093

-0.037

27

=

b

0.134

2.285

0.904

1.308

1.947

= x1

= x2

= x3

= x4

= x5

mxn

nxp

mxp

these must

match

Make sure and check the Analysis ToolPak Add-In from the Tools menu

to make the array formula functions available.

To use an array formula such as MMULT or MINVERSE, use the mouse

to select the whole range where the answers will go, type the command and

then use ctrl-shft-enter to set the command into the selected range.

…

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