Find an orthogonal basis for the column space of the matrix given below:

[ boldsymbol{ left[ begin{array}{ccc} 3 & -5 & 1 \ 1 & 1 & 1 \ -1 & 5 & -2 \ 3 & -7 & -8 end{array} right] }]This question aims to learn the Gram-Schmidt orthogonalization process. The solution given below follows the step-by-step procedure. In Gram-Schmidt orthogonalization, we assume the first basis vector […]

Find the rate of change of f at p in the direction of the vector u.

[f(x,y,z) = y^2e^{xyz}, P(0,1,-1), u = <frac{3}{13},frac{4}{13},frac{12}{13}>] This question aims to find the rate of change or gradient and projections of vector spaces onto a given vector. Read moreFind a nonzero vector orthogonal to the plane through the points P, Q, and R, and area of the triangle PQR.Gradient of a vector can be found using following […]