Question

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

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

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

Added by Matthew F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/10/2023

Step 1

Write down the coefficient matrix A and the right-hand side vectors B1 and B2 for both systems. For system (a): A = \begin{bmatrix} 4 & -3 \\ 4 & -5 \end{bmatrix}, B1 = \begin{bmatrix} 4 \\ 2 \end{bmatrix} For system (b): A = \begin{bmatrix} 4 & -3 \\ 4 & -5 Show more…

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