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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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
Transcribed Image Text:3. By the Gram-Schmidt process, obtain an orthonormal basis for R³ from the
ordered basis given by
--0--0--0
(9)
1,x²
=
=
=
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- (i) Give an example of two orthonormal vectors in R³. (ii) Using C=9 D=3 E=5 F=4 Schmidt process to find an orthonormal basis from the initial vectors () and (7). use the Gram- (iii) Construct a matrix which implements a shear of factor 3 along the first vector of your basis constructed in (ii), in that basis. Then use change of basis methods to give the corresponding (similar) matrix in the standard basis of R². Homeworkarrow_forwardFind a basis for Q(3^(1/3), 3^(1/2)) over Q.arrow_forwardFind the coordinate matrix of x relative to the orthonormal basis B in R". x = (10, 20, 5), B = {G) (-), (0, o, 1)} [x]g = 1 1arrow_forward
- 3. orthonormal basis B generated by B.arrow_forwardPlease can you help me with these two questions. I got it them both wrongarrow_forwardLet B={v_1...v_n} be some basis for R^n. Prove that if x is an element of R^n then x can be expressed as a linear combination of the basis vectors in a unique way. (i.e. if x=a_1v_1+...+a_nv_n and x=b_1v_1+...+b_nv_n then a_i=b_i for each i.)arrow_forward
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