Solve the system of linear equations using the inverse matrix .

Question

Solve the system of linear equations  using the inverse matrix  .

Quizplus · Accepted Answer

To solve the system using inverse matrix, we need to multiply the inverse matrix with the matrix of the coefficients of the variables, and then multiply the result with the matrix of the constants. The resulting matrix will give us the values of the variables. Using this method, we get the answer as:

[1, 2; 3, 4]^-1 * [5, 6; 7, 8] = [-1, 1; 1.5, -0.5]
[-1, 1; 1.5, -0.5] * [a, b; c, d] = [9, 10; 11, 12]

Solving this equation gives us:

a = -14
b = 15
c = 17.5
d = -18.5

So, the correct answer is A.

Solve the System of Linear Equations Using the Inverse