Question

Determine whether each of the following statements are true or false, where all the vectors are in R". Justify each answer. Complete parts (a) through (e) a. Not every linearly independent set in R" is an orthogonal set. OA True. For example, the vectors are linearly independent but not orthogonal OB. True. For example, the vectors are linearly independent but not orthogonal. O O C False. For example, in every linearly independent set of two vectors in R. one vector is a multiple of the other, so the vectors cannot be orthogonal D. False. Every orthogonal set is linearly independent b. If y is a linear combination of nonzero vectors from an orthogonal set, then the weights in the linear combination can be computed without row operations on a matrix OA you True. For each y in the weights in the linear combination y=Cu, + ... +cu, can be computed by 9 where j = 1, ..... O B. False. The weights in any linear combination can only be computed using row operations. OC. False. The weights in a linear combination can only be computed without row operations on a matrix if one of the vectors is the zero vector OD True. For each y in the weights in the linear combination y=Cu + +, u, can be computed by 9 voy where j=1...... c. If the vectors in an orthogonal set of nonzero vectors are normalized, then some of the new vectors may not be orthogonal O A True. Any time an orthogonal set of vectors is normalized then the new set is not orthogonal.

Answer 1

a Į Let alt] +alilo where a la are Scalary * 4+220 » 42-62 . . 2 420 -4+ (220 - 2 G=62 C 20 But 17:11]-[1] +[:] So, True.

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