Please answer both questions.

Question

A person has $200,000 invested partly at 3.25% and the rest 4.1%. The total yearly income from the two investments is $7265, and if you want to find out how much is invested at each rate b

 

A.) write the resulting system of equations as a matrix equation. 

B.) use inverse of a matrix to solve the equation 

Answer 1

Let x be the amount invested at 3.25 % and ($200,000 - x) be the rest invested at 4.1 % .

 

At the end of the year $7,265 = 0.0325 x + 0.041 ($200,000 - x) ---->

 

$7,265 = 0.0325 x + $8,200 - 0.041 x

 

$7,265 - $8,200 = 0.0325 x - 0.041 x

 

-$935 = -0.0085 x ----> -$935/-0.0085 = x ----> x = $110,000 ; $200,000 - $110,000 = $90,000

 

x = $110,000 invested at 3.25 %

y =  $ 90,000 invested at 4.1   %

 

A.)    1         x + 1       y = 200000

        0.0325 x + 0.041 y =    7265

 

         1               1       x        200000

                                         =        

          0.0325    0.041   y            7265

 

 

          AX = B ----> X = A^-1B

 

 B.)    x = $110,000

         y  = $ 90,000

 

          A^-1 is the inverse of matrix A

         

          Review your notes on how to find the inverse of a matrix. It's straightforward! It works ! Can't expand here ...