5 Solve the matrix equation 2 1 0 1 142 89 78 838 0 1 0 1 0

b Determine whether or not the vectors 1 1 1 1 2 3 and 2 1 1 form a basis for the vector space R c Solve the following system of equations by row echelon form 2x y 2z 8 3x 2y 4z 15 5x 4y z 1

H 2 and 2 Let T R2 R2 be the linear transformation satisfying T 51 18 and T 52 13 Find the image of an arbitrary vector x T

The velocity of a falling object is 12 4 m s at 2 seconds after being dropped and 22 2 m s at 3 seconds after being dropped Part A Graph the velocity of the falling object as a function of time in seconds Use t 0 to represent when the object was dropped 30 velocity m s 20 10 10 2 time seconds 3 Clear All Draw Part B Estimate when the object was falling with a velocity of 18 m s seconds

Which of these was not an outcome of the First Crusade O The establishment of the Crusader states O The formation of the Military Orders O The recovery of the Holy Land by the Byzantines O The building of massive castles in the Holy Land

The Crusade known as the Crusade of Kings was O The Third Crusade The Second Crusade The First Crusade The Fourth Crusade

Systems in Inree variables Use Cramer s Rule to solve each system 1 y z 2 3x y 3z 15 2x y 2z 7 2 A 1 2 2 C 2 2 1 B 3 3 1 D 1 3 3 A 3 2 0 C 3 3 3 2 x 2y 3z 7 x 3z 3 3x y 2z 7 B 2 3 2 D 0 1 1

A partial list of values for an linear function is given in the table shown Find the next three values if possible If not write NP in each box Round to the nearest integer if necessary 234 5 f x 1600 1520 9 7

Graph the following system of linear inequalities y 0 0 I O 8x 2y8 What are the corner points of the system 2x y Next find a point that is in the feasible set of the system but not on any of the boundary lines

Solve each system by elimination 1 2x 16 y 8y 8x 8 A 3 4 B 4 3 C 3 4 D 3 4 2 2 4y 4x 8 4x 8 4y A 2 4 B 4 2 C Infinite number of solutions D 2 4

Define the linear transformation T R Rm by T v Av Find the dimensions of R and Rm A dimension of Rn dimension of Rm