Tutorial 2 Solutions

Tutorial 2 Solutions - 3 Find the value(s of h for which...

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Tutorial 2, Solutions 1104 1-Last name: First name: 2-Last name: First name: 3-Last name: First name: 4-Last name: First name: 5-Last name: First name: ——————————————————————————— 1. Mark each statement True or False: a : T F : Row Echelon form is unique and reduced row echelon form is not unique. b : T F : The columns of any 5 × 6 matrix are linearly dependent. c : T F : The columns of a matrix A are linearly independent if the equation Ax = 0 has the trivial solution. d : T F : If A is an m × n matrix and if the equation A x = b is inconsistent for some b in R n , then A cannot have a pivot position in every row. Solution: a : ( F ) , b : ( T ) , c : ( F ) , d : ( T ) 2. Describe all solutions of A x = 0 in parametric form, where: A = 1 5 2 - 6 9 0 0 0 1 - 7 4 - 8 1 5 3 - 13 13 - 7 2 10 4 - 12 18 0 . Solution: A 1 5 2 - 6 9 0 0 0 1 - 7 4 - 8 0 0 0 0 1 0 0 0 0 0 0 0 . x = x 2 - 5 1 0 0 0 0 + x 4 - 8 0 7 1 0 0 + x 5 - 1 0 - 4 0 1 0 Note: The solution form may NOT unique.
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Unformatted text preview: 3. Find the value(s) of h for which the vectors are linear dependent: a : 2-4 1 , -6 7-3 , 8 h 4 b : 1-1-3 , -5 7 8 , 1 1 h Solution: a: for all values of h b: h =-10 4-Determine if the columns of the matrix form a linear independent set: A = 1-3 3-2-3 7-1 2 1-4 3 , B = -4-3 0-1 4 1 0 3 5 4 6 Solution : A: there are at most three pivot columns yet there are four variables, the equation Ax = 0 has a nontrivial solution (or the number of columns is more than the number of entries), so the columns of A are linearly dependent. B: Bx = 0 has only trivial solution (no free variable), so columns of B are linearly independent...
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Tutorial 2 Solutions - 3 Find the value(s of h for which...

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