Number 38 please and let2GEL24U2 =Uz =-11V, thendepen-sforma-1-42.-234dent setV1 =-1V2 =V3 =ndepen-3-6Find bases for H, K, and H + K. (See Exercises 33 and 34in Section 4.1.)that any that ifmendent,ws thatadеpen-nis case37. [M] Show that {t, sin t, cos 2t, sin t cos t} is a linearly inde-pendent set of functions defined on R. Start by assuming thatC i + C2 sin t + C3 cos 2t + C4 sint cos t 0(5)Equation (5) must hold for all real t, so choose severalspecific values of t (say, t 0, .1, .2) until you get a systemof enough equations to determine that all the c¡ must be zero.=1-ec;or why38. [M] Show that {1, cos t, cos² t,..., cos t} is a linearly inde-pendent set of functions defined on R. Use the method ofExercise 37. (This result will be needed in Exercise 34 inSection 4.5.)-t, anddepen-WEBPRACTICE PROBLEMSV2]. Row operations show that-2-2A =-20.33-90.of A contains a pivot position. So the columns of A do not span R',in Section 1.4. Hence {v1, v2} is not a basis for R. Since v and2, they cannot possibly be a basis for R2. However, since vi and v2inearly independent, they are a basis for a subspace of R, namely,A whose column space is the space spanned by {V1, V2, V3, V4}, ande A to find its pivot columns.6.2 -41-42 -42 -2 -80.204 -201-52.45

Name: Number 38 please and let2GEL24U2 =Uz =-11V, thendepen-sforma-1-42.-234
Uploaded: 2024-03-20T07:07:12.000Z
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Description: Number 38 please and let2GEL24U2 =Uz =-11V, thendepen-sforma-1-42.-234dent setV1 =-1V2 =V3 =ndepen-3-6Find bases for H, K, and H + K. (See Exercises 33 and 34in Section 4.1.)that any that ifmendent,ws thatadеpen-nis case37. [M] Show that {t, sin t, c