Question

b) Reduce the given quadratic form Q to its canonical form using orthogonal transformation = 2 + 3 2 + 3 2 − 2 and find its nature.

Answer 1

Answer:

64 is the answer.

Hope you understand well.

Answer 2

Answer:

I assume the question is to resolve a quadratic polynomial, perhaps:

Q = x1^2 + 2*x1*x2 + x2^2

into a quadratic form. That is, given Q, you want to recover the matrix H, such that

Q = [x1,x2]*H*[x1;x2]

This is quite easy using the symbolic toolbox. The desired matrix H is 1/2 times the Hessian matrix of Q.

For example, given the quadratic Q...

syms x1 x2

Q = x1^2 + 2*x1*x2 + x2^2

Q =

x1^2 + 2*x1*x2 + x2^2

X = [x1,x2];

H = hessian(Q)/2

H =

[ 1, 1]

[ 1, 1]

H is the desired matrix. We can see Q is recovered:

expand(X*H*X.')

ans =

x1^2 + 2*x1*x2 + x2^2

This is just an educated guess on my part as to the answer. Since there has been no response from the OP since it as first posted, we can only guess.