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Please I want the explanations and the answer and show work. Suppose a 5x7 matrix A has five pivot columns. Is Col A = R? Is Nul A = R?? Explain your answers. Is Col A = R5? OA. Yes. Since A has five pivot columns, dim Col A = 5. Thus, Col A is a five-dimensional subspace of R, so Col A is equal to R°. O B. No, Col A is not R5. Since A has five pivot columns, dim Col A = 2. Thus, ColA is equal to R2. O C. No. Since A has five pivot columns, dim Col A = 5. Thus, Col A is a five-dimensional subspace of R°, so Col A is not equal to R°. O D. No, the column space of A is not R. Since A has five pivot columns, dim Col A = 0. Thus, Col A is equal to 0. Is Nul A = R2? O A. Yes, Nul A is equal to R2. Since A has five pivot columns, dim Nul A = 2. Thus, Nul A is equal to R2. O B. No, Nul A is equal to R?. Since A has five pivot columns, dim Nul A = 0. Thus, Nul A is equal to0. VC. No, Nul A is not equal to R. It is true that dim Nul A = 2, but Nul A is a subspace of IR'. O D. No, Nul A is not equal to R?. Since A has five pivot columns, dim Nul A = 5. Thus, Nul A is equal to R°.

Please I want the explanations and the answer and show work. Suppose a 5x7 matrix A has five pivot columns. Is Col A = R? Is Nul A = R?? Explain your answers. Is Col A = R5? OA. Yes. Since A has five pivot columns, dim Col A = 5. Thus, Col A is a five-dimensional subspace of R, so Col A is equal to R°. O B. No, Col A is not R5. Since A has five pivot columns, dim Col A = 2. Thus, ColA is equal to R2. O C. No. Since A has five pivot columns, dim Col A = 5. Thus, Col A is a five-dimensional subspace of R°, so Col A is not equal to R°. O D. No, the column space of A is not R. Since A has five pivot columns, dim Col A = 0. Thus, Col A is equal to 0. Is Nul A = R2? O A. Yes, Nul A is equal to R2. Since A has five pivot columns, dim Nul A = 2. Thus, Nul A is equal to R2. O B. No, Nul A is equal to R?. Since A has five pivot columns, dim Nul A = 0. Thus, Nul A is equal to0. VC. No, Nul A is not equal to R. It is true that dim Nul A = 2, but Nul A is a subspace of IR'. O D. No, Nul A is not equal to R?. Since A has five pivot columns, dim Nul A = 5. Thus, Nul A is equal to R°.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please I want the explanations and the answer and show work. Suppose a 5x7 matrix A has five pivot columns. Is Col A = R? Is Nul A = R?? Explain your answers. Is Col A = R5? A. Yes. Since A has five pivot columns, dim Col A = 5. Thus, Col A is a five-dimensional subspace of R, so Col A is equal to R*. O B. No, Col A is not R5. Since A has five pivot columns, dim Col A = 2. Thus, ColA is equal to R2. O C. No. Since A has five pivot columns, dim Col A = 5. Thus, Col A is a five-dimensional subspace of R°, so Col A is not equal to R°. O D. No, the column space of A is not R5. Since A has five pivot columns, dim Col A = 0. Thus, Col A is equal to 0. Is Nul A = R2? O A. Yes, Nul A is equal to R2. Since A has five pivot columns, dim Nul A = 2. Thus, Nul A is equal to R2. O B. No. Nul A is equal to R?, Since A has five pivot columns, dim Nul A = 0. Thus, Nul A is equal to 0. C. No, Nul A is not equal to R. It is true that dim Nul A = 2, but Nul A is a subspace of IR'. O D. No, NulA is not equal to R?, Since A has five pivot columns, dim Nul A = 5, Thus, Nul A is equal to R5.
Transcribed Image Text:Please I want the explanations and the answer and show work. Suppose a 5x7 matrix A has five pivot columns. Is Col A = R? Is Nul A = R?? Explain your answers. Is Col A = R5? A. Yes. Since A has five pivot columns, dim Col A = 5. Thus, Col A is a five-dimensional subspace of R, so Col A is equal to R*. O B. No, Col A is not R5. Since A has five pivot columns, dim Col A = 2. Thus, ColA is equal to R2. O C. No. Since A has five pivot columns, dim Col A = 5. Thus, Col A is a five-dimensional subspace of R°, so Col A is not equal to R°. O D. No, the column space of A is not R5. Since A has five pivot columns, dim Col A = 0. Thus, Col A is equal to 0. Is Nul A = R2? O A. Yes, Nul A is equal to R2. Since A has five pivot columns, dim Nul A = 2. Thus, Nul A is equal to R2. O B. No. Nul A is equal to R?, Since A has five pivot columns, dim Nul A = 0. Thus, Nul A is equal to 0. C. No, Nul A is not equal to R. It is true that dim Nul A = 2, but Nul A is a subspace of IR'. O D. No, NulA is not equal to R?, Since A has five pivot columns, dim Nul A = 5, Thus, Nul A is equal to R5.
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