Show that u, v, and p are linearly independent-that is, none of the vectors is a linear combination of the other two. Three nonzero vectors u, v, and p are said to be linearly dependent if nonzero real numbers a and ẞ exist such that p = au + ẞv. Otherwise, the vectors are called linearly independent we must show that nonzero real numbers a and ẞ do not exist such that p = au + ßv. Thus, equating components in (0, -9, 17) a(1, 4, −7)+ B(2, -1, 4), we want to solve the following system. 0 -9 17 = a + 2ẞ 4α- B = -7α + 4ẞ The solution to this system is (a, b) = v, and pare = So (If an answer does not exist, enter DNE.) Thus, nonzero real numbers a and ẞ do not exist such that p = au + ẞv, so the vectors u, linearly independent.

Show that u, v, and p are linearly independent-that is, none of the vectors is a linear combination of the other two. Three nonzero vectors u, v, and p are said to be linearly dependent if nonzero real numbers a and ẞ exist such that p = au + ẞv. Otherwise, the vectors are called linearly independent we must show that nonzero real numbers a and ẞ do not exist such that p = au + ßv. Thus, equating components in (0, -9, 17) a(1, 4, −7)+ B(2, -1, 4), we want to solve the following system. 0 -9 17 = a + 2ẞ 4α- B = -7α + 4ẞ The solution to this system is (a, b) = v, and pare = So (If an answer does not exist, enter DNE.) Thus, nonzero real numbers a and ẞ do not exist such that p = au + ẞv, so the vectors u, linearly independent.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 46E

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