{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Mid2PracticeSol

Mid2PracticeSol - Math 20F A00 Linear Algebra Spring 2011...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 20F A00, Linear Algebra, Spring 2011 Practice Problems for Midterm Exam 2 1. Find all the co-factors, the adjugate matrix, and the determinant of the matrix 1 1 2 - 1 0 2 - 4 1 - 1 0 2 0 - 1 0 2 0 . 2. True or false: (a) Equivalent matrices have the same determinant; (F) (b) The determinant of any elementary matrix is 1; (F) (c) det( A + B ) = det A + det B , det( - A ) = - det A, and det( AB ) = (det A )(det B ); (F, F, T) (d) det A T = det A and det A - 1 = (det A ) - 1 ; (T, T) (e) A square matrix is invertible if and only if its determinant is nonzero. (T) 3. Calculate the determinant of each of the following matrices: 5 0 - 1 1 - 3 - 2 0 5 3 ; 1 1 2 - 1 0 0 - 4 0 - 1 3 12 0 1 2 - 4 1 ; 1 3 3 - 4 0 1 2 5 2 5 4 - 3 - 3 - 7 - 5 2 . 4. Show that det 1 1 1 a b c a 2 b 2 c 2 = ( a - b )( b - c )( c - a ). (Hint: transpose, row reduction, and expan- sion.) 5. Let A,B,C be three 2 × 2 matrices. Show that det bracketleftbigg A 0 B C bracketrightbigg = (det A )(det C ). 6. What is Cramer’s rule? Let A be a 3 × 3 matrix and assume det A = 2, the co-factors C 11 = 2, C 12 = - 4, C 13 = 6. What is the solution to
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}