Let $A = \begin{bmatrix} -41 & -78 & 24 \\ 21 & 40 & -12 \\ 0 & 0 & 1 \end{bmatrix}$. Find an invertible matrix $P$ and a diagonal matrix $D$ such that $D = P^{-1}AP$.
Added by Andrea M.
Close
Step 1
Step 1: First, we need to find the eigenvalues and eigenvectors of the given matrix A. Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 65 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
Let A = [[-1, 28, 42], [0, -5, -6], [0, 4, 5]]. Find an invertible matrix P and a diagonal matrix D such that D = P^-1 AP. P = , D =
Madhur L.
Let A = [32 -70 -140; 5 -13 -20; 5 -10 -23]. Find an invertible matrix P and a diagonal matrix D such that D = P-1AP.
$21-28=$ Finding Determinants Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. $$ \left[ \begin{array}{rrrr}{1} & {2} & {0} & {2} \\ {3} & {-4} & {0} & {4} \\ {0} & {1} & {6} & {0} \\ {1} & {0} & {2} & {0}\end{array}\right] $$
Matrices and Determinants
Determinants and Cramer's Rule
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