Answer Happy

Help please. I attached an example step-by-step below. Don't dothe example, just use it as reference
Find an orthogonal basis for the column space of the matrix to the right. An orthogonal basis for the column space of the given matrix is (Type a vector or list of vectors. Use a comma to separate vectors as needed.) C -1 6 2-8 1 -2 7 1 -4 -3 5 4
Find an orthogonal basis for the column space of the matrix to the right. and x₂ to find V₂- Recall that V₂ = x2 X2 *V1 -v₁. Compute the inner products that appear in this formula. First compute X₂ *V₁. V₁ *V₁ X₂ V₁ = (5)(-1)+(-6)(3) + (− 1)(2) + (-5)(1) = - 30 Next compute v₁ •V₁. V₁V₁=(-1)(-1) + (3)(3) + (2)(2)+(1)(1) = 15 -1 01 5 7 4 3-6 2 -1 7 1 -5 -4
Substitute -30 for x₂ V₁, 15 for V₁ V₁, and the vectors x₂ and v₁ into the formula for v2. X2 *V1 V1.₁ V₂=X2- ' -6 -1 -5 5 -5 Simplify this result. 5 +2 -1 -30 3 15 -1 3 N 1 N 1 W 0 3 - 3
This means that V₂ = Use X3 - 1 4-H V₁ and V₂- 2 1 X3 *V2 V2 *V2 V3 = X3 -4 3 0 X3 *V1 V₁ •V₁ w 3 3 - 3 to find V3 using the formula shown below.
Compute the inner products that appear in this formula. First compute X3 V₁. X3 V₁ = (7)(-1) + (4)(3) + (7)(2) + (− 4)(1) = 15 Recall that v₁ V₁ = 15. Compute X3 *V2- X3 V₂ = (7)(3) + (4)(0) + (7)(3) + (− 4)(-3) = 54 Compute V₂ *V₂. V₂ V₂ = (3)(3) + (0)(0) + (3)(3) + (− 3)(-3) = 27
Substitute 15 for X3 *V₁, 15 for v₁ •V₁, 54 for x3 *V₂, 27 for v₂V₂, and the vectors X3, V₁, and v₂ into the formula for V3. 1 V3 = x3 || X3 *V1 V₁ *V₁ 7 15 7 15 4 Simplify this result. 2 1 X3 *V₂ V2 *V2 -1 3 2 1 - 3 54 27 3 0 3 - 3
This means that = V3 N and so an orthogonal basis for the column space of the given matrix is V T 3 N m 3 3 N - 1