Given the traffic flow diagram below (with numbers representing vehicles per hour): 100 100 X₁ X5 X₂ 50 100 X3 50 (a) Write out a linear system equivalent to this flow pattern. (b) Write out the matrix of coefficients and the augmented matrix that corresponds to your system in part (a). Note: you do not have to solve this system.

4. Tickets for a soccer game are $6 for adults and $4 for students. At the last game there were 220 tickets sold and $1064 collected. Write a system of linear equations to represent this situation and then use matrices to solve for the number of adult tickets sold and the number of student tickets sold at the last soccer game.

Ms. Henry borrowed a total sum of $56,000 from her bank and her credit union.  The bank charged an annual interest rate of 11% while the credit union charged an annual interest rate of 9%.  If the total yearly interest payment was $5560, how much did she borrow from the credit union? (a)  Define the variables you use and write the system of equations that represents the above problem. (b) Write the augmented matrix of the linear system.

Solve the following system of linear equations: 3x1-3x2-3x3 -3 -3x1+6x2 = 0 -x1-2x2+4x3 = 5 If the system has no solution, demonstrate this by giving a row-echelon form of the augmented matrix for the system. You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. The system has a unique solution The system has no solution The system has a unique solution The system has infinitely many solutions x3

Let us consider the following system of equations. fx+2y=3 [2x+ y = 3 Write this system in a matrix form Ax=b. Find the rank of the following matrices: rank(A)= rank([4 | b])=_

A Sillall software corporation borrowed $115,000 to expand its software line. The corporation borrowed some of the money at 3%, some at 4%, and some at 5%. Use a system of equations to determine how much was borrowed at each rate when the annual interest was $5,300 and the amount borrowed at 4% was times the amount borrowed at 3%. Solve the system using matrices. amount borrowed at 3% amount borrowed at 4% $ amount borrowed at 5% Need Help? Master It Read It Submit Answer

Provide an augmented matrix of a system of linear equations having exactly the following solution: x = 5-6t y=-21+10t z = −3+2t You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. 000 000 000