Math 330 Quiz 4.6 March 27,2009 Give explanations to your answers for each of the following: 1. If A is an 8 × 3 matrix whose Null space has dimension 1, then what is the dimension of the row space of A ? What is the dimension of the column space of A ? SOLUTION: The dimension of the row space and the dimension of the column space (i.e. the rank of A ) are the same. This is equal to the number of columns of A minus the dimension of the Null space i.e. 3-1 = 2. 2. If A is an 8 × 3 matrix whose Null space has dimension 1, then when we row reduce A to reduced Echelon form, how many zero rows will we get? (Does this depend on other features of A ? If so, how?) SOLUTION: In reduced Echelon form, the non-zero rows of A will form a basis for the row space of A . Since this has dimension 2, there will be just two nonzero rows. Since A has 8 rows, we will get 8-2 = 6 rows which are all zero. 3. If A is a 16 × 33 matrix, then what is the largest possible dimension for Col A ? SOLUTION:
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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.