hw5.pdf - Linear Algebra Fall 2018 HW#5 Please give complete well-written solutions to the following exercises Show all work to relieve full credit

# hw5.pdf - Linear Algebra Fall 2018 HW#5 Please give...

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Linear Algebra - Fall 2018 HW #5 Please give complete, well-written solutions to the following exercises. Show all work to relieve full credit! Total number of points: 65 (+10 extra credit) I adapted the shape of the homework sheet a bit for them to be a better preparation for the second midterm and final. (1) (3 points (0.5 each)) Fill in the blanks (a) Let A be a 10 × 7 matrix with rank 5. Then the dimension of C ( A ) is and the dimension of C ( A T ) is . (b) The nullspace N ( A ) and the row space C ( A T ) are subspaces of R n . Every vector x N ( A ) is perpendicular to every of A . (c) Let a 1 , . . . , a n be independent vectors in R m and let b R m . The projection p of b onto the subspace spanned by a 1 , . . . , a n is given by p = . It is the vector in that subspace that is to b . (2) (9 points) Let A = 1 2 3 4 5 6 7 8 9 . a) (3 points) Determine a basis of the nullspace N ( A ). b) (2 points)Find the dimensions of the four subspaces N ( A ) , C ( A ) , C ( A T ) and N ( A T ).

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• Spring '14
• Li
• Linear Algebra, Total Number of points, row space C

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