Linear Algebra Questions and Answers

Find the slope and y intercept of the following equation 10x 2y 260 0 slope y intercept

Determine which property of determinants the equation illustrates 3 1 4 00 0 0 97 8 O If one row of a matrix is a multiple of another row then the determinant of the matrix is zero O If one row of a matrix consists entirely of zeros then the determinant of the matrix is zero If two columns of a matrix are interchanged then the determinant of the matrix changes sign O If a row of a matrix is multiplied by a scalar then the determinant of the matrix is multiplied by that scalar O none of these

Use either elementary row or column operations or cofactor expansion to find the determinant by hand Then use a software program or a graphing utility to verify your answer 0 1 10 1 1 90 1 9 10 5 1

Let A and B be square matrices of order 3 such that A 6 and B 9 a Find ABI b Find 2A c Are A and B singular or nonsingular Explain O A and B are both singular because they both have nonzero determinants O A and B are both nonsingular because they both have nonzero determinants OA is singular but B is nonsingular because A B OB is singular but A is nonsingular because A BI d If A and B are nonsingular find A1 and B 1 If the inverse is undefined enter UNDEFINED A 1 B e Find AB 1

Find AI IBI A B and IA B Then verify that A B A BI 1 30 A a b B c A B B 1 3 0 11

Determine whether each statement is true or false J a The break even point occurs where the total revenue function is first equal to the total cost function OTrue False b If lim f x and lim f x both exist then lim f x also exists x a x a x a True False c If lim f x does not exist then lim f x does not exist x a x a True False d According to the law of demand p d x is an increasing function True False e If lim f x does not exist then lim f x does not exist x at x a True False

Consider the position function s t 16t2 92t representing the position of an object moving vertically along a line Sketch a graph of s with the secant line passing through 0 25 s 0 25 and 2 s 2 Determine the slope of the secant line and explain its relationship to the moving object A 120 22 0 25 Q Q 5 B 120 22 0 25 Type an integer or a decimal The slope of the secant line is msec What is the relationship of the slope to the moving object Q Q 57 OA The slope is the average velocity of the object over the interval 0 25 2 OB The slope is the instantaneous velocity when t 2 C The slope is the average velocity of the object over the interval 22 120 OD The slope is the maximum velocity of the object O C 120 22 0 25 EN Q Q G

Compute each of the following derivatives a 10x dx b 4x3 4 dx 30 0 x dx