# Linear equation (Matrix)

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
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
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:
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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