Consider the matrix P = I_( 3)-(x*x)/(|x|^2 ), where I_(3 )denotes the 3 * 3 matrix. Which of the following adjectives describes P : symmetric, antisymmetric, square, diagonal. Write down all applicable answers
Added by Michael W.
Step 1
Step 1: First, let's determine the properties of the given matrix P. Show more…
Show all steps
Close
Your feedback will help us improve your experience
Jiva Y and 62 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Compute the eigenvalues of the 3 x 3 matrix A = [1 1 1; 1 1 1; 1 1 1]. Find an invertible matrix P such that the matrix D = P-1AP is diagonal.
Jiva Y.
For each of the following symmetric matrices $A,$ find an orthogonal matrix $P$ and a diagonal matrix $D$ such that $P^{\prime} A P$ is diagonal: (a) $A=\left[\begin{array}{rr}1 & 2 \\ 2 & -2\end{array}\right]$ (b) $A=\left[\begin{array}{rr}5 & 4 \\ 4 & -1\end{array}\right]$ (c) $A=\left[\begin{array}{rr}7 & 3 \\ 3 & -1\end{array}\right]$
Liliane M.
Suppose $A=P R P^{-1},$ where $P$ is orthogonal and $R$ is upper triangular. Show that if $A$ is symmetric, then $R$ is symmetric and hence is actually a diagonal matrix.
Symmetric Matrices and Quadratic Forms
Diagonalization of Symmetric Matrices
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD