math54 - quiz 3 - solns - -1 4 1 8 1 8 3 16 3. Mark the...

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Math 54 quiz 3 Solutions 1. (4 points) Calculate the determinant, using any method you like ± ± ± ± ± ± ± ± 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 ± ± ± ± ± ± ± ± Let’s use cofactor expansion along the first column. This gives (+1) det 1 0 1 1 1 0 1 1 1 as the only term. Next we can use the algorithm for 3 × 3 matrices to obtain 1 + 0 + 1 - 1 - 0 - 0 = 1 . 2. (3 points) Find the inverse of the matrix A below. (Again any method is fine) ² -3 2 2 4 ³ We will row reduce the matrix below ² -3 2 1 0 2 4 0 1 ³ ² 1 10 1 2 2 4 0 1 ³ ² 1 10 1 2 0 -16 -2 -3 ³ ² 1 10 1 2 0 1 2 16 3 16 ³
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± 1 0 - 1 4 1 8 0 1 1 8 3 16 ² So, we obtain
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Unformatted text preview: -1 4 1 8 1 8 3 16 3. Mark the following as true or false. No justication is needed. (1 pt each) (a) If A is a square matrix, and A x = b has a unique solution for some b, then det A 6 = 0. TRUE (b) The matrix 1 1-1 2 1-2 1 3 1-3 4 1-4 1 is invertible. FALSE (c) If A and B are square matrices of the same size, det AB = det BA . TRUE...
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This note was uploaded on 09/17/2011 for the course MATH 54 taught by Professor Chorin during the Spring '08 term at University of California, Berkeley.

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math54 - quiz 3 - solns - -1 4 1 8 1 8 3 16 3. Mark the...

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