eng77-Spring_2006-mt2-Segapunta-soln

# eng77-Spring_2006-mt2-Segapunta-soln - Page 1 of 9 E77...

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Page 2 of 9 E77 Midterm 2/Student ID: ______________________________ A. Linear Algebra (15 points ) 1. (+3) 451 12 15 8 xy 0 += = What is the determinant of the coefficient matrix of these equations? __ , det( ) ______________ AA ⎛⎞ == ⎜⎟ ⎝⎠ A= [-4,5;12,-15] det(A) = 0 Does this set of equations have a unique solution? Y E S N O NO 2. (+4) For what value of a will the following set have a solution in which both x and are nonzero? Find the relationship between y x and y 40 36 0 xa y = ______, ___________, ____________ ax y = a=8; x=2*y; y=0.5*x 3. (+4) a. (+0.5) What MATLAB function calculates the determinant of a matrix A? _____ det(A) ____________________________________________________________ b. (+1) Does the matrix A above have to be square? (Circle one choice) YES NO YES c. (+1) What does the backslash (\) operator do:
Page 3 of 9 E77 Midterm 2/Student ID: ______________________________ 1) For an n -by- n system of linear equations? _ Solves for a linear equation defined by A*X = B; X=A\B 2) For an m -by- n ( m>n ) system of linear equations? _ Solves using least squares the over-determined system: A*X=B; X=A\B d. (+1) What MATLAB function calculates the inverse of a matrix?

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## eng77-Spring_2006-mt2-Segapunta-soln - Page 1 of 9 E77...

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