Question

(4) (a) Find an $$LU$$ factorization of $$A = \begin{bmatrix} 5 & 1 & 4 \\ 25 & 8 & 28 \\ 30 & 15 & 42 \end{bmatrix}$$ (b) Let $$T$$ be the linear map transformation whose standard matrix is $$A = \begin{bmatrix} 1 & 3 & 2 \\ 0 & 1 & 4 \\ 0 & 0 & 1 \\ 1 & 4 & 6 \\ 2 & 7 & 8 \end{bmatrix}$$ Does $$T$$ maps $$R^3$$ onto $$R^5$$? Is $$T$$ a one-to-one mapping?

Name: 4 a find an lu factorization of a beginbmatrix 5 1 4 25 8 28 30 15 42 endbmatrix b let t be the linear map transformation whose standard matrix is a beginbmatrix 1 3 2 0 1 4 0 0 1 1 4 6 2 7 41607
Uploaded: 2023-11-30T23:52:07-08:00
Duration: 21 min 22 s
Channel: Oswaldo Jiménez
Description: 4 a find an lu factorization of a beginbmatrix 5 1 4 25 8 28 30 15 42 endbmatrix b let t be the linear map transformation whose standard matrix is a beginbmatrix 1 3 2 0 1 4 0 0 1 1 4 6 2 7 41607

          (4) (a) Find an $$LU$$ factorization of
$$A = \begin{bmatrix} 5 & 1 & 4 \\ 25 & 8 & 28 \\ 30 & 15 & 42 \end{bmatrix}$$
(b) Let $$T$$ be the linear map transformation whose standard matrix is
$$A = \begin{bmatrix} 1 & 3 & 2 \\ 0 & 1 & 4 \\ 0 & 0 & 1 \\ 1 & 4 & 6 \\ 2 & 7 & 8 \end{bmatrix}$$
Does $$T$$ maps $$R^3$$ onto $$R^5$$? Is $$T$$ a one-to-one mapping?

4 a find an lu factorization of a beginbmatrix 5 1 4 25 8 28 30 15 42 endbmatrix b let t be the linear map transformation whose standard matrix is a beginbmatrix 1 3 2 0 1 4 0 0 1 1 4 6 2 7 41607

Added by Julia F.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Oswaldo Jiménez

11/30/2023

Step 1

Given matrix: $$A = \begin{bmatrix} 5 & 1 & 4 \\ 25 & 8 & 28 \\ 30 & 15 & 42 \end{bmatrix}$$ Step 2: Perform row operations to get zeros below the first pivot. $$R_2 \leftarrow R_2 - (25/5)R_1 = R_2 - 5R_1$$ $$R_3 \leftarrow R_3 - (30/5)R_1 = R_3 - 6R_1$$ The Show more…

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(4) (a) Find an $$LU$$ factorization of $$A = \begin{bmatrix} 5 & 1 & 4 \\ 25 & 8 & 28 \\ 30 & 15 & 42 \end{bmatrix}$$ (b) Let $$T$$ be the linear map transformation whose standard matrix is $$A = \begin{bmatrix} 1 & 3 & 2 \\ 0 & 1 & 4 \\ 0 & 0 & 1 \\ 1 & 4 & 6 \\ 2 & 7 & 8 \end{bmatrix}$$ Does $$T$$ maps $$R^3$$ onto $$R^5$$? Is $$T$$ a one-to-one mapping?