Exam 4: Systems of Linear Equations; Matrices

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM: -A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 annual income from the investments, how much should the bank invest in each?Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount invested in mortgages.

Perform the operation, if possible: -

State whether the matrix is in reduced form or not in reduced form: -

Solve using Gauss-Jordan elimination: -

Perform the indicated row operations on the following matrix: -

Determine which of the following matrix equations represents the solution to the system:.

Use Gauss-Jordan elimination, without introducing fractions, to find the inverse of .

Perform the indicated row operations on the following matrix: -

Find the inverse, if it exists, of the given matrix: -

Use the given encoding matrix A to solve the problem: -Use the given message to construct the code matrix by assigning numbers to the letters and symbols. Use the numerical assignment a = 1, b = 2, . . . , z = 26, space = 30, period = 40, and apostrophe = 60.Message: CALL ME TOMORROW.Encoding matrix A =

The input-output matrix for an economy is Find the internal consumption.

The matrix is the final matrix form for a system of two linear equations in variables and . Write the Solution of the system: -

Given the matrix B: What is the size of B?

The matrix is the final matrix form for a system of two linear equations in variables and . Write the Solution of the system: -

Solve the system as matrix equations using inverses: -

Suppose that the supply and demand equations for a logo sweat shirt in a particular week are for the demand equation; and , for the supply equation. Find the equilibrium price and quantity.

Write a system of equations associated with the augmented matrix. Do not try to solve: -

If a and b are nonzero real numbers and

Solve the equation for the indicated variable. Assume that the dimensions are such that matrix multiplication and addition are possible and that inverses exist when needed: -Solve for C: CZ = Y