Solve the Equation Ax = B by Using the LU

question 26

Multiple Choice

Solve the equation Ax = b by using the LU factorization given for A.
- $$A = \left[ \begin{array} { r r r r } 1 & 2 & 4 & 3 \\- 1 & - 3 & - 1 & - 4 \\2 & 1 & 19 & 3 \\1 & 5 & - 9 & 7\end{array} \right] , \mathbf { b } = \left[ \begin{array} { l } 2 \\0 \\4 \\3\end{array} \right]$$
$$A = \left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \\- 1 & 1 & 0 & 0 \\2 & 3 & 1 & 0 \\1 & - 3 & - 2 & 1\end{array} \right] \left[ \begin{array} { r r r r } 1 & 2 & 4 & 3 \\0 & - 1 & 3 & - 1 \\0 & 0 & 2 & 0 \\0 & 0 & 0 & 1\end{array} \right]$$

• A) \(\mathbf { x } = \left[ \begin{array} { r } 27 \\ 9 \\ 8 \\ - 3 \end{array} \right]\)
• B) \(\mathbf { x } = \left[ \begin{array} { r } 27 \\ - 18 \\ 89 \\ - 13 \end{array} \right]\)
• C) \(\mathbf { x } = \left[ \begin{array} { c } 41 \\ - 6 \\ - 3 \\ - 5 \end{array} \right]\)
• D) \(\mathbf { x } = \left[ \begin{array} { r } 2 \\ - 2 \\ 8 \\ - 3 \end{array} \right]\)

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Definitions:

Commercial Bribes

Illicit payments or gifts given to influence the actions or decisions of someone in a business or official position, typically considered illegal or unethical.

Secure New Business

The act of acquiring new clients or customers for a company or a firm, often through marketing, networking, or outreach efforts.

Inferior Product

A product deemed to be of lower quality or lesser value when compared to others of its kind in the market, often associated with poor construction or defects.

Identity Theft

The theft of a form of identification, such as a name, date of birth, or Social Security number, which is then used to access the victim’s financial resources.