Jump to level 1 Let (U₁=[2₁2] ₂-[-1818)-[3]} U3 = 0 Use the Gram-Schmidt process to find an orthogonal basis under the Frobenius inner product. Orthogonal basis: V₁ a = Ex: 5 b: 0 0 a 1.59 * {v₁ = [²₁₂2] ·M = [8 -¹8]. ³₁ = [1185 2]} V₂ V3 -1 -1.65 Ex: 5 0 C = Ex: 1.23 be a basis for a subspace of R2x2. d=Ex: 1.23

V =R * R 10a6b T(") - (170-100) {(2)· (3)} B = { find the matrix representation of T with respect to beta. Then determine wether beta is a basis consisting of eigenvectors. I have got -2 [T]₁ = ( 2 4 this does not match answer key. What's wrong? please point it out and have the rest of solution to the problem. thanks!

Question 13 of 13 -/1 Let Rª have the Euclidean inner product. Use the Gram-Schmidt process to transform the basis {u1, u2, U3, U4, } into an orthonormal basis. U1= (0,2,1,0), u2 = (1, – 1,0,0), u3 = (1,2,0, – 1), u4 = (3,0,0,3) %3D %3D %3D 1 1 1 5 1 5 2 5 65V 6 5 91 = 92 = 5 1 5 2 |5 5 1 5 2 5 93 = Võ3 V 6 5V6 ). 4 = 5 1 4 2 5 V6'5 6 1 1 %D 92 I| 9^ 9^ 9^ 51 5 2 6' 3 ▼ 6'5 V 6 5 1 5 2 5 6' 5 V 6'5V 6' 93 4 %D 94 = 152 5V6 5 1 1 92 5 5 152 1 6' 5 6'5V6 5 1 5 2 [5 93 = 94 = 3 V6 51 1 5 2 5 5 92 = 65V 91 0, V5' V5 2 3 (tVtV - V - V). 94 = %3D 93 V15' V15 V15 V15

Let S = = span {x¹ = x3 4 (a) Use Gram-Schmidt process to find an orthogonal basis {u¹, u², u³} of S. (b) Find an orthonormal basis {q¹, q², q³} of S.