{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

F10PracMT2 - M341 Fall 10 Practice Midterm 2 First...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
M341, Fall 10. Practice Midterm 2. First Name ......................... Last Name (PRINT) ............................... - Calculators are authorized. Books, hand written notes or other documents are not authorized. - Show all your work. If you use a calculator, you are not waived of the intermediary computations that are still to be shown. - Explain every answer, either by a computation, or by using a theorem. Cor- rect results with no explanation will not be taken into account. - Freely use both sides of the sheets. - Put your name on any additional or unstapled sheet. Problem 1. 1) Compute the determinant of the matrix: A = 3 2 1 1 6 3 2 4 0 . Is A invertible and why? 2) What is the adjoint or adjugate matrix of A ? What is the inverse of A ? (Show all your work. A correct explanation of what is a cofactor and what is the adjoint matrix might redeem small computational mistakes.) 3) Compute the inverse of A by a row reduction method. 4) Solve the linear system (You have the choice of the method, but explain your choice): 3 x 1 + 2 x 2 x 3 = 6 x 1 + 6 x 2 + 3 x 3 = 30 2 x 1 4 x 2 = 8 Solution 1
Image of page 1

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

View Full Document Right Arrow Icon
3 2 1 1 6 3 2 4 0 = 0 16 10 1 6 3 0 16 6 = 4 0 8 5 1 6 3 0 8 3 = 4( 1) × 8 1 5 1 3 = ( 1)[4 × ( 16)] = 64 . Since det A ̸ = 0, the matrix A is invertible. The matrix of minors ( A i,j instead of a i,j ) is: 12 6 16 4 2 16 12 10 16 No need of a calculator, all the matrices are 2x2 with small integers as entries. Of course the less confident you are in your computations, the more intermediaries you must show for partial credit. Anyway, results without a sufficient explanation on how you got them will certainly not provide you with the full grade even if corret. The matrix of cofactors is obtained by replacing the A i,j by the ( 1) i + j A i,j : 12 6 16 4 2 16 12 10 16 . Finally the Adjugate or Adjoint matrix is the transpose of the matrix of cofactors. A = 12 4 12 6 2 10 16 16 16 . In this problem, you are asked to give the adjoint matrix so the inverse must be computed by the formula A - 1 = 1 det A Adj( A ). The row reduction method would not be relevant since you know A .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern