H23-1 - Math 330 Homework 2.3 (Pages 132,133) In all...

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Unformatted text preview: Math 330 Homework 2.3 (Pages 132,133) In all exercises unless stated otherwise, the matrices indicated are square (i.e. as many rows as columns). (6) Use as few steps as possible to decide if the following matrix is invertible: 1- 5- 4 3 4- 3 6 SOLUTION: The key to checking if the matrix is invertible, is to make sure that every column is a pivot column. Seeing whether or not this is the case, simply involves moving to Echelon (not reduced Echelon) form. Since we are not attempting to find the inverse, we dont need to augment by the identity: R 3 R 3+3 R 1 = 1- 5- 4 3 4- 9- 12 R 3 R 3+3 R 2 = 1- 5- 4 3 4 Therefore, we only have two pivots so this matrix is not invertible. (8) Use as few steps as possible to decide if the following matrix is invertible: 1 3 7 4 0 5 9 6 0 0 2 8 0 0 2 10 SOLUTION: R 4 R 4- R 3 = 1 3 7 4 0 5 9 6 0 0 2 8 0 0 0 2 Now we have a matrix in Echelon form with a pivot in every column. Hence this matrix is invertible. (12) TRUE or FALSE The student should be reminded that all matrices are assumed to be square. The validity of these statements is very different if we do not assume this....
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This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.

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H23-1 - Math 330 Homework 2.3 (Pages 132,133) In all...

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