7 22 points previous answers holtlinalg1 43023

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7. 2/2 points | Previous Answers HoltLinAlg1 4.3.023. Suppose that A is a matrix and that If T is one-to-one, then what is the dimension of the null space of A 0 12 × 7 T ( x ) = A x ker( T ) = 0 , dim(ker( T )) = 0. ? 0 Solution or Explanation Since T is one-to-one, and Hence rank( A ) = 2. A = 5 1 0 3 0 1 x 8 1 0 4 1 x = ~ 5 1 0 3 0 1 x 8 1 0 4 1 2 1 0 3 0 1 x 8 0 0 x 4 0 1 5 rank( A ) = 2, x = 20 . 9 × 16 rank( A ) = m nullity( A ) = 16 10 = 6 . .
8. –/1 pointsHoltLinAlg1 4.3.024. Suppose that A is a matrix and that If T is onto, then what is the dimension of the null space of A ? and . , 4 .
9. 1/1 points | Previous Answers HoltLinAlg1 4.3.030. Suppose that A is a matrix and that B is an equivalent matrix in echelon form. If B has one pivot column, what is 3 × nullity( A )? 3 Solution or Explanation since the rank of A is the number of pivot columns of B . 10. 1/1 points | Previous Answers HoltLinAlg1 4.3.034. Suppose that A is an matrix, with and col( A ) a subspace of R 5 . 5 × nullity( A )? 4 3 , ,
What are the dimensions of A ? ( n , m ) = m = rank( A ) + nullity( A ) = 3 + 5 = 8 . col( A ) 5 is × 8 .
11. 1/1 points | Previous Answers HoltLinAlg1 4.3.046. Determine if the statement is true or false, and justify your answer. If A and B are equivalent matrices, then row( A ) = row( B ). True, by the theorem that says if A and B are equivalent matrices, then the subspace spanned by the rows of A is the same as the subspace spanned by the rows of B . .

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