Consider the following two systems. (a) (b) (i) Find the inverse of the (common)

Question

Consider the following two systems.
(a)

(b)

(i) Find the inverse of the (common) coefficient matrix of the two systems.

Consider the following two systems. { -5x - 3y = -3 2x - 7y = -3 { -5x - 3y = -1 2x - 7y = 4 Find the inverse of the (common) coefficient matrix of the two systems. A-1 = [ ] Find the solutions to the two systems by using the inverse, i.e. by evaluating A-1B where B represents the right hand side (i.e. B=[-3 -3] for system (a) and B = [-1 4] for system (b)) Solution to system (a): x = y Solution to system (b): x = y

Explanation / Answer

coefiiceinet matrix

A = [ -5, -3 ]

      [ 2 , -7]

|A| = 35 -(-6) = 41

A^-1 = [ -7/41     2/41 ]

             [   -3/41      -5/41]

B =   [ -3   1]

         [ -3 4 ]

A^-1* B =

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