Exam 7: Matrix Algebra

If A = and B = ,find 2A - 3B.

If A = and B = ,find -4A + 5B.

An economy is based on two sectors,agriculture and manufacturing.Production of a dollar's worth of agriculture requires an input of $0.40 from agriculture and $0.10 from manufacturing.Production of a dollar's worth of manufacturing requires an input of $0.20 from agriculture and $0.30 from manufacturing.Find the output for each sector that is needed to satisfy a final demand of $16 billion for agriculture and $32 billion for manufacturing.

Use matrix multiplication to represent the system:

Perform the indicated operation and simplify your answer: [6][5]

Use the matrix operations on a graphing calculator to show that A + C = C + A.

Solve the following system of equations by reducing the matrix:

On Saturdays,the company must move 23 tons of mail,16 tons of medical supplies,and 17 tons of freight.This system of equations can be represented by the matrix: .Reduce this matrix to calculate how many aircraft of each type should be used.

Use the matrix operations on a graphing calculator to find her income if increasing it by 20% would cause an increase in profit of 50%.(Round to the nearest thousand dollars.)

Solve the matrix equation: =

Without solving,determine whether the following system of linear equations has a unique solution,or infinitely many solutions.

If A = and C = ,find AC.

If ,then

Let A = .Find .

and

For one animal,she determines that she needs to combine these bags to get 9000 g of ,19,000 g of ,and 17,000 g of )Use the matrix operations on a graphing calculator to determine how many bags of each type of food should she order.

Solve by the method of reduction:

If A = ,B = ,and C = ,find 3C + BA.

If A = ,B = ,and C = ,find 4A - 2B + 3C.

Use the encoding matrix an additional coding 1 matricx plus the matrices to answer the question. -EF