Solving Matrix

Question

a) the sum of two numbers is 37. the secound number is 3 more than the first number. write a system of equations to represent the given information

 

b) write a matric equation for the system equations

 

c) what are the two numbers?

Answer 1

So in regular algebra, the equations would be

 

x+y=37

y=x+3

 

or

 

x+y = 7

-x+y=3

 

augmented matrix is just the coefficients

 

⌈    1    1       37⌉

⌊    -1   1       3  ⌋

 

you want 1 0

              0 1

 

So keep the first row and then add the two rows for your new second row

 

⌈   1    1        37  ⌉

⌊   0     2       40  ⌋

 

Then divide row 2 by 2 to get

 

⌈   1     1      37  ⌉

⌊   0     1      20  ⌋

 

now replace the first row with row 1 - row 2 to get the remaining 0, which results in

 

⌈     1     0    17   ⌉

⌊     0     1    20   ⌋

 

So x = 17 and y = 20.

 

Hope this helped.