Using Matrices, solve the following: A practical Humber student invested 20,000 in two stocks. The two stocks yielded 7% and 11% simple interest in the first year. The total interest received was $1,880. How much does the student invested in each stock?

Anish Buchanan 2020-11-27 Answered
Using Matrices, solve the following: A practical Humber student invested 20,000 in two stocks. The two stocks yielded 7% and 11% simple interest in the first year. The total interest received was $1,880. How much does the student invested in each stock?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Sadie Eaton
Answered 2020-11-28 Author has 104 answers
Step 1
Let x be the amount invested at 7%
y be the amount invested at 11%
Total amount invested = 20000
Thus, x+y=20000 ...(1)
Interest received at 7% =0.07x
Interest received at 11%=0.11y
Total interest received =1880
Thus, 0.07x+0.11y=1880 ...(2)
step 2
Hence we have two system of equations
x+y=20000
0.07x+0.11y=1880
we solve it by matrices
It can be expressed as
[110.070.11][xy]=[200001880]
Augmented Matrix for Ax=b is
[11200000.070.111880]
R2R20.07R1[11200000.070.111880]
Which can be expressed as
x+y=20000
0.04y=480
y=12000 And, x=2000012000=8000 Hence [xy]=[800012000]
Step 3
ANSWER:The student invested 8,000 at 7% interest and 12,000 at 11% interest
Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-01-31
Find a basis for the space of 2×2 diagonal matrices.
Basis ={[],[]}
asked 2021-02-08
Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.
asked 2021-06-18

Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer's rule. Use each method at least once when solving the systems below. include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable.
2x+3y+4z=3
4x+2y6z=2
4x+3z=0

asked 2021-02-24
Write the set in the form {x|P(x)}, where P(x) is a property that described the elements of the set. {a,e,i,o,u}.
asked 2021-11-19
Use the given of the coefficient matrix to solve the following system.
7x1+3x2=6
6x13x2=4
A1=[11273]
asked 2021-02-03
Which of the following statements are always true, with A and B are orthogonal matrices?
1)det(AT(A+B)BT)=det(AT+BT)
2)det(A1+BT)=det(AT+B1)
3)det(A+BT)=det(AT+B)
asked 2020-11-23
Find the product AB of the two matrices listed below:
A=(213224134)
B=(121234)