Quick question with matrices

  • Thread starter EvilPony
  • Start date
  • Tags
    Matrices
In summary, Sid Carrington had investments in a savings account, mutual funds, and bonds, earning a total annual interest of $21300. His bond investment was three times his savings account investment, and the interest earned on his bonds was equal to the dividends received from his mutual fund investment. The amounts he invested in each type of investment are: $x in a savings account, $y in mutual funds, and $3x in bonds.
  • #1
EvilPony
18
0
ok here is the question

The annual interest on Sid Carrington's three investments amounted to $21300: 5% ona savings account, 9% on mutual funds, and 11% on bonds.If the amount of Sid's investment in bonds was triple the amount of his investment in the savings account, and the interest earned from his investment in bonds was equal to the dividends he received from his investment in mutual funds, find how much money he placed in each type of investment.


? $ in a savings account
? $ in mutual funds
? $ in bonds

I set up the matrix as

.05 .09 .11 21300
3 0 -1 0
0 1 -1 0

and when I do rref on it I keep getting the wrong answer

would be great if I could get some help on this within 45 minutes


:shy:
 
Physics news on Phys.org
  • #2
Your last line is wrong. The mutual fund investment is not equal to the bond investment. It's the income earned on each of them that is equal.
 
  • #3


Hi there,

Thank you for reaching out with your question. It seems like you have set up the matrix correctly, but there may be an error in your calculations. Here is the correct solution:

Let x be the amount invested in the savings account, y be the amount invested in mutual funds, and z be the amount invested in bonds.

From the given information, we know that:

0.05x + 0.09y + 0.11z = 21300 (equation 1)
z = 3x (equation 2)
0.11z = 0.09y (equation 3)

Substituting equation 2 into equation 3, we get:

0.11(3x) = 0.09y
0.33x = 0.09y
y = 3.67x

Substituting this into equation 1, we get:

0.05x + 0.09(3.67x) + 0.11(3x) = 21300
0.05x + 0.33x + 0.33x = 21300
0.71x = 21300
x = 30000

Therefore, the amount invested in the savings account is $30,000, the amount invested in mutual funds is $110,100, and the amount invested in bonds is $90,000.

I hope this helps! If you need further assistance, please let me know. Good luck with your calculations!
 

What is a matrix?

A matrix is a rectangular array of numbers or symbols arranged in rows and columns. It can be used to represent data or to solve equations in mathematics and science.

What is the purpose of using matrices?

Matrices are used for various purposes in mathematics, science, and engineering. They can be used to represent data, solve systems of equations, transform geometric shapes, and perform operations in linear algebra.

How do you add or subtract matrices?

To add or subtract matrices, the matrices must have the same dimensions. Then, you simply add or subtract the corresponding elements in each matrix to get the resulting matrix. For example, to add two 2x2 matrices A and B, you would add the top left elements of A and B to get the top left element of the resulting matrix, and so on.

What is the identity matrix?

The identity matrix is a square matrix with 1s on the main diagonal and 0s everywhere else. When multiplied by another matrix, the identity matrix acts as the number 1 does in regular multiplication - it leaves the other matrix unchanged.

How do you multiply matrices?

To multiply matrices, the number of columns in the first matrix must match the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix. To find the elements of the resulting matrix, you multiply the corresponding elements of each row in the first matrix by the corresponding elements of each column in the second matrix, and then add the products.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
  • Precalculus Mathematics Homework Help
Replies
16
Views
4K
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • General Math
Replies
1
Views
3K
Replies
1
Views
3K
Replies
9
Views
2K
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top