Alg 2 (BJU) L4-5 Notes/HW2 -- Inverse Matrices & Solving Systems

L4-5 Notes/HW2: Solving Systems Using Inverse Matrices

(Review)
Systems of Equations with Matrices

Notice the equations are written in standard form. Every coefficient must be represented and in the corresponding row and column. If a variable is not present in an equation, the coefficient for that spot would be ZERO.

(NEW) How to solve using inverses (Can't Divide by a Matrix)

Instead of dividing by the coefficient matrix, A, MULTIPLY BY THE INVERSE to solve for the variable matrix, X.

It is ALWAYS the inverse of the coefficient matrix multiplied by the constant matrix.

(See Ex. 4 & 5 on pp. 169-170 of the textbook for additional help.)

Multiple Choice

Write the matrix equation for the system.

Fill in the Blank

Find the determinant for the coefficient matrix.

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Multiple Choice

Use the determinant of -7 to find the inverse for the matrix.

Fill in the Blank

Multiply the inverse by the constant matrix to solve for x.

***Note: There is a typo in the image. The constant matrix should have a -2 beneath the 8, as it does in the previous questions, rather than a 2. Please use -2 for your calculations.***

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Fill in the Blank

Multiply the inverse by the constant matrix to solve for y.

Multiple Choice

Identify the coefficient matrix for the following system.

Fill in the Blank

At a local movie theater, a person purchased 2 large popcorn and 4 large drinks for a total of $38.50 before taxes. A second person purchased 1 large popcorn and 3 large drinks for $25.10 before taxes at the same theater. How much is the theater charging for large popcorn?(Use a matrix equation to solve)

Fill in the Blank

At a local movie theater, a person purchased 2 large popcorn and 4 large drinks for a total of $38.50 before taxes. A second person purchased 1 large popcorn and 3 large drinks for $25.10 before taxes at the same theater. How much is the theater charging for large drink?(Use a matrix equation to solve)

Fill in the Blank

Calculate the determinant

Multiple Choice

What is the inverse of this matrix?

• _{(1/25)  (-4/25)
  (3/25)  (13/25)}
• _{(1/5)  (-4/5)
  (3/5)  (13/5)}
• _{(6/25)  (-2/25)
  (2/25)  (9/25)}
• _{(1/150)  (-4/150)
  (3/150)  (13/150)}