Question

I REALLY NEED HELP IM ON A TIME

The matrix equation represents a system of equations.

A matrix with 2 rows and 2 columns, where row 1 is 2 and 3 and row 2 is 1 and 2, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 5 and row 2 is 4.


Solve for x and y using matrices. Show or explain all necessary steps.

Answer 1

x=2 and y=3.

Explanation:

We can solve this by multiplying the inverse of the matrix on the left side of the equation with the matrix on the right side of the equation. The inverse of a 2x2 matrix is given by:

[a b]^-1 = 1/(ad-bc) [d -b]

[-c a]

So we can find the inverse of the matrix on the left side of the equation as follows:

[2 3]^-1 = 1/(2*2-3*1) [2 -3] = [-2 3]

[-1 2]

Multiplying this with the matrix on the right side of the equation gives us:

[-2 3] [5] [x]

[-1 2] [4] = [y]

Which can be written as:

-2x + 3y = 5

-x + 2y = 4

We can solve this system of equations using substitution or elimination. Let’s use substitution. From the second equation, we can write:

x = 2y - 4

Substituting this into the first equation gives us:

-2(2y-4) + 3y = 5

-4y + 8 + 3y = 5

-y = -3

y = 3

Substituting this value of y into either of the equations gives us:

x = 2(3) - 4

x = 2

so

x=2 and y=3.