What property must a symmetric 3 × 3 matrix have in order for the equation xTAx...

What property must a symmetric 3 × 3 matrix have in order for the equation x^TAx = 1 to represent an ellipsoid? (6 points)(Kindly provide a long, comprehensive proof)

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genius_generous answered 2 years ago

b) a matrix is skew symmetric if AT=-A.If A is a skew-symmetric matrix of odd order,show...

b) a matrix is skew symmetric if AT=-A.If A is a skew-symmetric matrix of odd order,show that A is not invertible c)Let A and B be n*n matrixes with detA=detB not equal to 0,If a and b are non zero real numbers show that det (aA+bB-1)=det(aB+bA-1)

Suppose A is an n × n matrix with the property that the equation Ax =...

Suppose A is an n × n matrix with the property that the equation Ax = b has at least one solution for each b in R n . Explain why each equation Ax = b has in fact exactly one solution

What property must emulsifiers have that fats lack?

A square matrix A is said to be symmetric if its transpose AT satisfies AT= A,...

A square matrix A is said to be symmetric if its transpose AT satisfies AT= A, and a complex-valued square matrix A is said to be Hermitian if its conjugate transpose AH = (A)T = AT satisfies AH = A. Thus, a real-valued square matrix A is symmetric if and only if it is Hermitian. Which of the following is a vector space? (a) The set of all n xn real-valued symmetric matrices over R. (b) The set of all...

Create a square, almost symmetric 4 X 4 matrix B with values 1, 2, 3 and...

Create a square, almost symmetric 4 X 4 matrix B with values 1, 2, 3 and 4 on the diagonal. Let values off diagonal be between 0.01 and 0.2. Almost symmetric matrix is not a scientific term. It just means that most of the off diagonal terms on transpose positions are close in value: 1. Determine matrix BINV which is an inverse of matrix B; 2. Demonstrate that the matrix multiplied by its inverse produces a unit matrix. Unit matrix...

Show that, given any 3 integers, at least 2 of them must have the property that...

Show that, given any 3 integers, at least 2 of them must have the property that their difference is even.

Show that the hat matrix is idempotent (i.e. by showing that ?2 = ?) and symmetric.

What are the 3 questions that a buyer or seller must answer yes to in order...

What are the 3 questions that a buyer or seller must answer yes to in order to be considered a merchant

Problem 3. Throughout this problem, we fix a matrix A ∈ Fn,n with the property that...

Problem 3. Throughout this problem, we fix a matrix A ∈ Fn,n with the property that A = A∗. (If F = R, then A is called symmetric. If F = C, then A is called Hermitian.) For u, v ∈ Fn,1, define [u, v] = v∗ Au. (a) Let Show that K is a subspace of Fn,1. K:={u∈Fn,1 :[u,v]=0forallv∈Fn,1}. (b) Suppose X is a subspace of Fn,1 with the property that [v,v] > 0 for all nonzero v ∈...

Let A be a 2×2 symmetric matrix. Show that if det A > 0 and trace(A)...

Let A be a 2×2 symmetric matrix. Show that if det A > 0 and trace(A) > 0 then A is positive definite. (trace of a matrix is sum of all diagonal entires.)

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