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3. Do the vectors (1, 1,0, 0), (1, -1,0,0), (0, 0, -1, 1) and (0, 0, -1, –1) form an orthogonal basis of R4? Is this basis orthonormal? Let u = (u1, U2, U3, U4) be a vector in R4. Find the values of a1, a2, a3 and a4 such that u = a1(1, 1,0, 0) + a2(1, –1,0,0) + a3(0,0, –1, 1) + a4(0,0, –1, –1).

3. Do the vectors (1, 1,0, 0), (1, -1,0,0), (0, 0, -1, 1) and (0, 0, -1, –1) form an orthogonal basis of R4? Is this basis orthonormal? Let u = (u1, U2, U3, U4) be a vector in R4. Find the values of a1, a2, a3 and a4 such that u = a1(1, 1,0, 0) + a2(1, –1,0,0) + a3(0,0, –1, 1) + a4(0,0, –1, –1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Do the vectors (1, 1,0, 0), (1, -1,0,0), (0, 0, –1, 1) and (0, 0, -1, –1) form an orthogonal basis of R4? Is this basis orthonormal? Let u = (u1, U2, U3, U4) be a vector in R4. Find the values of a1, a2, a3 and a4 such that u = a1(1, 1,0, 0) + a2(1, –1,0,0) + a3(0,0, –1, 1) + a4(0,0, –1, –1).
Transcribed Image Text:3. Do the vectors (1, 1,0, 0), (1, -1,0,0), (0, 0, –1, 1) and (0, 0, -1, –1) form an orthogonal basis of R4? Is this basis orthonormal? Let u = (u1, U2, U3, U4) be a vector in R4. Find the values of a1, a2, a3 and a4 such that u = a1(1, 1,0, 0) + a2(1, –1,0,0) + a3(0,0, –1, 1) + a4(0,0, –1, –1).
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