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# HW3 - for which solutions exist c Let x 1 = 1 x 2 = 2 x 3 =...

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Applied Multivariate Analysis I EDUC 771 Problem Set 3 1. Using the matrix X below X = 1 2 1 4 1 2 1 2 2 5 1 0 1 0 3 3 1 0 5 2 2 1 3 1 7 ! " # # # # # # \$ % & & & & & & Determine if the rows/columns are linearly independent. How do you know? What is the rank of the matrix? 2. Let A = 1 1 0 0 1 0 1 0 1 0 0 1 ! " # # # \$ % & & & = μ ( 1 ( 2 ( 3 ! " # # # # \$ % & & & & c = 4 6 5 ! " # # # \$ % & & & a. Write the equation A β =c as a set of three equations. b. What is the rank of A ? What does that tell you about the number of unique unknowns
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Unformatted text preview: for which solutions exist? c. Let x 1 = + ! 1 , x 2 = + 2 , x 3 = + 3. Write the equation A " = c in the form B x = d . What is B? Solve for x . d. Let x 1 = + 1 , x 2 = 2 " 1 , x 3 = 3 " 1. Write the equation A # = c in the form B x = d . What is B? Solve for x . e. Let i = ( 1 + 2 + 3 )/ 3. Explain why ( 1 " i ) + ( 2 " i ) + ( 3 " i ) =...
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