Advanced Algebra II Notes 6.4 Solving Systems with Inverse Matrices

Solve the system of equations using elimination: 2x + y = 55x + 3y = 13 Write the system as the product of a coefficient matrix and a

variable matrix equal to a constant matrix.

This equation is a matrix form of ax = b What is the multiplicative identity? What is the identity matrix for State the identity matrices for each dimension: 1x1 2x2 3x3 4x4

34

12

Find the inverse matrix for

34

12][A

Solve the given system using an inverse matrix: 2x + 3y = 7 x + 4y = 6

On a recent trip to the movies, Duane, Marsha, and Parker each purchased snacks. Duane bought two candy bars, a small drink, and two bags of popcorn for a total of $11.85. Marsha spent $9.00 on a candy bar, two small drinks, and a bag of popcorn. Parker spent $12.35 on two small drinks and three bags of popcorn, but no candy. (poor Parker, no candy). If all the prices included tax, what was the price of each item?

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