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- Find the value of k for which the points (5,7) , (k,5) , and (0,2) are collinear. Please solve this for me!!-13/27] -4/27 -4/9 5/9 -20/27] -2/27 Let v₁ = √2 = and √3 = Find a vector in IR4 such that -20/27 ' ' -2/9 17/27 4/9 -2/3 2/9 {1, 2, 3, 4} is an orthonormal set. Answer:(5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A + B)-B = B(A + B)~'A %3D (b). A(A+ B)-1B (A-1+B-)-1
- 5. Locate the numbers z₁+z₂ and z₁ - z₂ vectorially when z, = 2i, z₂ = 2/3 -i.Find the set of ordered pairs (xo, yo) for which Picard's Theorem guarantees that the IVP y' = computations to support your answer. ry I+2 y (xo) = yo has a unique solution. Show all necessaryFind the stable vector of P = 2 2 2 3 -|3
- Assignmort -1- .Ao Find the domain of the following Fune tions :- 1. Fx) = J4-12X 2. X- 25 3. gck) = J27-3x + X-10 x²_4 X+2 2 4. hcx) 5. ge) =/ x+ 4 x - 32Let M-{1, 2}. Then O IP(MXM)I=4 None of the mentioned MxM=(1, 4) M×M={(1,1),(2,2)} O IP(MxM)|=163. Give an example of an orthonormal set with 4 non-trivial vectors in R'.
- 3. Find orthonormal vectors q₁ and 42 in the plane spanned by a = vector in this plane is closest to (0, 1, 2, 1)? (3, 2,5, 1) and b = (4, 3, 8, 3). Whichlse the eigenfucten expausien welboud to Selve the vibrating string Problem Pole: Utt =4 uxx +e sinzx ,ocxcRitzo Bcs: ucot) = ulkit) = 0I t>o ICs: ucx,o) = Sinx , uŁCXrc) = sinzs, osks-7 4 -4 4 Let T = 3 -7-4-1 -6 A nonzero vector with integer entries in the null space of T'is 00000