3 Let u1 = 0 , u₂ = -3 B-B-Q} , U3 = be a basis for R³. Use the Gram-Schmidt process to find an orthogonal basis under the Euclidean inner product. Orthogonal basis: 3 0 - {~= B] - B] = 0}} V1= = α 0 , V3 b a = Ex: 5 b = Ex: 5 c = Ex: 5
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- Do the vectors v1 = (-3, 7) and v2 = (5, 5) form a basis for R²?Find the coordinate vector of [3, -4, 7] relative to the ordered basis B= ([1, 0, 0], [0, 0, 1], [2, 4, 0]) of R^3. Justify your work.Find the coordinate vector of p relative to the basis S = P1; P2» P3 } for P,. p = 5 – 7x + 4x²; p, 1, р, 3 х, Рз = x?. (p)s= ( ).
- Determine the following three vectors {<2,1,0>, <4,2,2>, <-2,-1,3>} forms a basis for R^3. Expalain your answer.tion 4 of 12 > Calculate the cross product. (9j - 5k) x (2j+ k) (Give your answer using standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) ai + bj + ck = lu Transcendentals PubDoes the ordered set v, v, va form a basis for R^3? If not, which vectors would you subtract from the set and which standard basis vector can you add to the set to make it a basis for R^3? vi = (1,–1, –2) = (5, –4, –7) v = (-3, 1,0) Select all answers that are correct. O subtract vector v 1 from the set O no it does not form a basis for R^3 O subtract vector v_3 from the set O yes it forms a basis for R^3 O add vector e_1 O add vector e 2 subtract vector v_2 from the set O add vector e_3
- Ui3D(1,2,7,3.2) u3=13,27,13,2) 44=(1,4,6,97) ) ۱۹ رگگلرگادک = 11S Find a basis of 'w> consisting of the original Given Vectors.and Find dimw.Find the change-of-coordinate matrix P from B to C and P from C to B for the bases B = {1,t,t^2} and C = {1+t,t+t^2,1+t^2}.Determine three of the given vectors that form a basis for space (R^3) and express the fourth vector as a linear combination of these basis vectors. p=[1,1,- 1], q= [-1,1,1], r= [1,3,-1], s = [1,1,0]
- How do I find the basis for these two vectors?List five vectors in Span/v,, v2}. Do not make a sketch. -6 V1 1 V2 %3D - 5 List five vectors in Span{v1, V2} (Use the matrix template in the math palette. Use a comma to separate vectFind the coordinate vector of = --8 = B 5 -1 with respect to the basis B= 0 {} for R³.