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aS FAST as possible please! please provide a typewritten solution i would be grateful! PROBLEM 1. SOLVE ONLY PART (d)
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- Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner product p,q=a0b0+a1b1+a2b2+a3b3. An Orthonormal basis for P3. In P3, with the inner product p,q=a0b0+a1b1+a2b2+a3b3 The standard basis B={1,x,x2,x3} is orthonormal. The verification of this is left as an exercise See Exercise 17..Find a basis for R3 that includes the vector (1,0,2) and (0,1,1).
- In Problems 21–26, decompose v into two vectors v1 and v2 , where v1 is parallel to w, and v2 is orthogonal to w. 25. v = 3i + j, w = - 2i - jFind a basis of solutions by the frobenius method. Xy'' + 2y' + xy = 0How can I find a basis for KerT of the attached function? I know that T is linear but how do I find the KerT and therefore the basis?
- 5)Find the terminal point of the vector that is equivalent to u = (1, 2) and whose initial point is A(1, 1).Find a standard basis vector that can be added to the set (v1, v2} to produce a basis of R^3. v1 = (1, -1, 0) and v2 = (3, 1, -2) I've tried this, but I found that e1, e2, and e3 form det = 0. Is it right that e1, e2, e3 meet all the requirements?Let {u1, u2} be an orthonormal basis for C2, and letz = (4 + 2i)u1 + (6 − 5i)u2. Determine the value of ||z||.
- Let u1 = 1 2 3, u2 = 1 −2 1, u3 = 4 1 −2, and y = 1 −3 11(a) Show that {u1, u2, u3} is an orthogonal basis for R3.(b) Express y as a linear combination of u1, u2, and u3.(c) Normalize u1, u2, and u3 to produce an orthonormal basis {v1, v2, v3} for R3For part b) do we need to check whether the list (x, x, x/2) is also linearly independent? Since a basis of V is a list of vectors in V that is linearly independent and spans V and we know that span = (x, x, x/2) there is also the requirement of linear independence?Can you find the basis of N(T) and the basis for R(T) ?