Please solve these matrix problems The 3D vectors a and b ar

Please solve these matrix problems

The 3-D vectors a and b are defined as: a={1 4 6}^T and b = {4 7 2}^T Calculate the scalar product c = a b Use a and b from problem 1. along with T =[1 7 2 3 4 3 6 5 7] to calculate the following products: Ta and b^T Ta Consider the matrix equation [A]{x} = {b} given by [2 -1 0 -1 2 -1 0 -1 2]{x_1 x_2 x_3} = {4 0 4} Construct the quadratic form F(x) = {x}^T [A]{x} -2{x}^T{b} Write out the equation set that defines the extreme value of F(x). in the form Ax=b (Recall from calculus that the extreme of a function are found by setting derivatives to zero. For a function of multiple variables, this means setting the partial derivatives to zero.) Solve to find the values of x which extremist F(x) Find the extreme value of .F(x)

Solution

#Question1

The transpose of both matrices \'a\' and \'b\' will be 1 X 3 (after takig transpose). If you wanna multiply both matrices, the no. of columns of first matrix should be equla to the no. of rows of second matrix. Since the above condition is not satisfied, the matrix multiplication is not possible.