For the Given Matrix A, Find a Basis for the Corresponding

question 19

Multiple Choice

For the given matrix A, find a basis for the corresponding eigenspace for the given eigenvalue.
- $A = \left[ \begin{array} { r r r } - 4 & 0 & 0 \\ - 10 & 6 & 0 \\ - 30 & 16 & - 2 \end{array} \right] , \lambda = - 4$

• A)
• \(\left\{ \left[ \begin{array} { r } 1 \\ - 1 \\ - 7 \end{array} \right] \right\}\)
• B)
• \(\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 0 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 0 \\ - 7 \end{array} \right] \right\}\)
• C)
• \(\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 7 \end{array} \right] \right\}\)
• D)
• \(\left\{ \left[ \begin{array} { l } 1 \\ 1 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 1 \\ 0 \\ 7 \end{array} \right] \right\}\)

---

Definitions:

Decision-making Process

The cognitive process leading to the selection of a belief or course of action among several possible alternative options.

Market

Definition: A defined area or arena in which commercial dealings occur, including buying, selling, and exchange of goods or services.

Content Analysis

A research technique used to systematically analyze the content of communication, such as texts or media, to understand its themes or patterns.

Sentiment Analysis

The process of using computational tools to identify, extract, quantify, and study affective states and subjective information from text.