(a) Use the given information to write a system of linear equations for x, y, and z. (b) Convert this system to an augmented matrix. (c) Use a spreadsheet and Gaussian elimination with matrices to find the amount that was invested at each interest rate. Include two screenshots: (1) the formula view (or put in front to keep them from evaluating) of your spreadsheet (2) the results.
(a) Use the given information to write a system of linear equations for x, y, and z. (b) Convert this system to an augmented matrix. (c) Use a spreadsheet and Gaussian elimination with matrices to find the amount that was invested at each interest rate. Include two screenshots: (1) the formula view (or put in front to keep them from evaluating) of your spreadsheet (2) the results.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve b and c part only in 30 min
Transcribed Image Text:Solution
a) let x be the amount invested in the 3% account.
y be the amount invested in the 4% Account and
z be the amount invested
in the 5%. account.
According to the question,
x+y+z = (a+b+c+900) x 1000
=>
·x+y+z
= 1000 a +1000 b + 1000 € + 900000
Also, Total annual interest on the three investment was
$(C+720) x 50
xx3x1
gx4xi
= 500 +720x50
+2x5x1
100
100
100
→
3x +
(2)
+4y+52 =
+52 = 5000c + 3600000
Also, Twice as much
is invested at 3%
money
invested at 5%
2x = Z
2x - 2 = 0
linear
.. The required system of
x+y+z
2 = 1000 a +10006 +1000c + 900000
3x + 4y + 5z = 5000 C +3600000
2x
-N
+
as
equations for x, y, z ore
Transcribed Image Text:2. Taika invested a total of $ (a + b + c + 900) x 1,000 into three investment accounts, paying
3%,4%, and 5% simple interest per year. The annual interest earned on the three investments
was $ (c + 720) x 50. Twice as much money is invested at 3% as invested at 5%.
Let x be the amount invested in the 3% account,
and z be the amount invested in the 5% account.
y be the amount invested in the 4% account,
O
0
(a) Use the given information to write a system of linear equations for x, y, and z.
(b) Convert this system to an augmented matrix.
(c) Use a spreadsheet and Gaussian elimination with matrices to find the amount that was
invested at each interest rate.
Include two screenshots:
SS
(1) the formula view (or put in front to keep them from evaluating) of your spreadsheet
(2) the results.
Note: (Using methods other than Gaussian Elimination will result in heavy mark losses.
You need to convert your matrix into row-echelon form.)
(d) Check your answer for part (c) by substituting your solutions into the system of equations.
N
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