# Practice Midterm 2 Solution.pdf - Practice Midterm 2...

• Test Prep
• 7

This preview shows page 1 - 4 out of 7 pages.

The preview shows page 2 - 4 out of 7 pages.
Math 54PracticeMidterm2SolutionsSeptember27,20181. (10 points) LetA=111010. Find a 3 by 2 matrixBsuch thatAB=1001.abcdefand multiplying gives the system:a+c+e= 1
Math 54Practice Midterm 2 SolutionsSeptember27,20182. (10 points) Consider the following matrix:A=21-101104001-21011(a) (3 points) Find the determinant of A.
(b) (4 points) Is A invertible? If so, findA-1.(c) (3 points) Use parts a and b to find all solutions toA~x=
Page 2
Math 54Practice Midterm 2 SolutionsSeptember24,20183. (10 points) Label the following statements as either true or false.(a) (2 points) Every matrix can be row reduced into a unique row echelon form.(b) (2 points) IfAis a square matrix with det(A) = 2, then det(A-1) =12.(c) (2 points) IfT:RnRmis an injective linear transformation, thenn < m.(d) (2 points) Any collection ofkvectors inRncontaining the zero vector is a linearly dependent set.(e) (2 points) LetAbe annbynmatrix such thatA2=A, thenAis invertible.

Course Hero member to access this document

Course Hero member to access this document

End of preview. Want to read all 7 pages?

• • • 