Question

Let $A = \begin{bmatrix} 48 & -20 \\ 100 & -42 \end{bmatrix}$ \\ Find a matrix $S$, a diagonal matrix $D$ and $S^{-1}$ such that $A = SDS^{-1}$. \\ $S = \begin{bmatrix} \Box & \Box \\ \Box & \Box \end{bmatrix}$, $D = \begin{bmatrix} \Box & \Box \\ \Box & \Box \end{bmatrix}$, $S^{-1} = \begin{bmatrix} \Box & \Box \\ \Box & \Box \end{bmatrix}$

          Let $A = \begin{bmatrix} 48 & -20 \\ 100 & -42 \end{bmatrix}$ \\ Find a matrix $S$, a diagonal matrix $D$ and $S^{-1}$ such that $A = SDS^{-1}$. \\ $S = \begin{bmatrix} \Box & \Box \\ \Box & \Box \end{bmatrix}$, $D = \begin{bmatrix} \Box & \Box \\ \Box & \Box \end{bmatrix}$, $S^{-1} = \begin{bmatrix} \Box & \Box \\ \Box & \Box \end{bmatrix}$

Let A =
< b m a t r i x >
Find a matrix S, a diagonal matrix D and S^-1 such that A = SDS^-1.
S =
< b m a t r i x >, D =
< b m a t r i x >, S^-1 =
< b m a t r i x >

Added by Susana J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Melissa Munoz

03/05/2024

Step 1

To find the eigenvalues, we solve the characteristic equation det(A - λI) = 0, where I is the identity matrix. det(A - λI) = det([[48,-20],[100,-42]] - λ[[1,0],[0,1]]) det(A - λI) = det([[48-λ,-20],[-100,-42-λ]]) det(A - λI) = (48-λ)(-42-λ) - (-20)(-100) det(A - Show more…

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Let A=[[48,-20],[100,-42]] Find a matrix S, a diagonal matrix D and S^(-1) such that A=SDS^(-1). 48 20 Let A 100 42 Find a matrix S, a diagonal matrix D and S-1 such that A = SDS-1 S