Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Unitary Method
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Speed, Time, and Distance
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Number 30
is {1, t, t2,t} for the eigenvalues of A. Verify this statement for the case when A is diagonalizable. e transformation 27. Let V be R" with a basis B = {b1, ..., b,}; let W be R" with the standard basis, denoted here by ɛ; and consider the identity transformation I : R" → R", where I(x) = x. Find the matrix for I relative to B and E. What was this matrix called in Section 4.4? 28. Let V be a vector space with a basis B = {b,..., b,}, let W be the same space V with a basis C = {c...., c,}, and let I be the identity transformation I : V → W. Find the matrix for I relative to B and C. What was this matrix called in Section 4.7? = Ax. Find a nal. 29. Let V be a vector space with a basis B = {bj,..., b,}. Find the B-matrix for the identity transformation I: V →V. [M] In Exercises 30 and 31, find the B-matrix for the transforma- tion x→ Ax where B = {b1, b2, b3}. b1 = Г6 -2 -2 30. А — | 3 1 -2 |, |2 -2 Ax. hat A is not b1 = 1 , b2 = 1, b3 = 3 is a 3 x 3 -7 -48 -16 31. A = 1 14 6. exist a basis nal matrix? -3 -45 -19 -3 -2 1, b2 = b1 = -3 b3 are square. = invertible 3 for some 32. [M] LetT be the transformation whose standard matrix is given below. Find a basis for R with the property that [ T ]R is diagonal. en find an -6 9. -3 A = -1 -2 1 is similar -4 4 0. 4.
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Transcribed Image Text:is {1, t, t2,t} for the eigenvalues of A. Verify this statement for the case when A is diagonalizable. e transformation 27. Let V be R" with a basis B = {b1, ..., b,}; let W be R" with the standard basis, denoted here by ɛ; and consider the identity transformation I : R" → R", where I(x) = x. Find the matrix for I relative to B and E. What was this matrix called in Section 4.4? 28. Let V be a vector space with a basis B = {b,..., b,}, let W be the same space V with a basis C = {c...., c,}, and let I be the identity transformation I : V → W. Find the matrix for I relative to B and C. What was this matrix called in Section 4.7? = Ax. Find a nal. 29. Let V be a vector space with a basis B = {bj,..., b,}. Find the B-matrix for the identity transformation I: V →V. [M] In Exercises 30 and 31, find the B-matrix for the transforma- tion x→ Ax where B = {b1, b2, b3}. b1 = Г6 -2 -2 30. А — | 3 1 -2 |, |2 -2 Ax. hat A is not b1 = 1 , b2 = 1, b3 = 3 is a 3 x 3 -7 -48 -16 31. A = 1 14 6. exist a basis nal matrix? -3 -45 -19 -3 -2 1, b2 = b1 = -3 b3 are square. = invertible 3 for some 32. [M] LetT be the transformation whose standard matrix is given below. Find a basis for R with the property that [ T ]R is diagonal. en find an -6 9. -3 A = -1 -2 1 is similar -4 4 0. 4.
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