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Unformatted text preview: M340L: Matrices and Matrix Calculations Unique Number: 57160 Practice Final sketchy Solution, May , 2006 LAST NAME (PRINT)................................. First Name ....................................... Calculators are authorized. Books, hand written notes or other documents are not authorized. Show all your work. 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. Good Luck. I. Let A = 1 3 2 1 1 1 1 0 1 1 0 1 2 1 1 1 2 3 1 2 2 3 . 1) What is the domain of A ? What is the codomain of A ? (3points) The domain of A is R 6 , number of columns of A . The codomain of A is R 4 , number of rows of A . Observe that the words source and target are rather used for the linear mapping T (see question 3)), the words domain and codomain are more usual for the matrix. 2) Give an echelon form for A . Give the reduced echelon form of A . 1 A = 1 3 2 1 1 1 1 0 1 1 0 1 2 1 1 1 2 3 1 2 2 3 1 3 2 1 1 0 1 1 1 1 0 0 1 1 3 3 0 0 3 1 3 2 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 3 0 0 1 3 2 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 The reduced echelon form is 1 0 1 0 0 2 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 . You were expected to show more work than I do. 3) Is the mapping T : x 7 A x onetoone? No it is not because there are non pivot columns, so the homogeneous equation A x = has non trivial solutions. Is it onto? (Justify your answers, Yes or No is not acceptable) Yes it is because there is a pivot in each row. 4) Without further calculation give the Rank of A and the dimension of the null space of A . (Justify your answers.) Rank A = 4 is the dimension of Col( A ) (or the dimension of the range of T ) that is the number of pivot columns....
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This note was uploaded on 02/26/2012 for the course MATH 340L taught by Professor Seckin during the Spring '11 term at University of Texas at Austin.
 Spring '11
 SECKIN
 Matrices

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