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Suppose a 5x8 matrix A has two pivot columns. Is Col A =R2? Is Nul A=R6? Explain your answers. Is Col A =R²? OA. No, the column space of A is not R2. Since A has two pivot columns, dim Col A=3. Thus, Col A is equal to R³ OB. Yes. Since A has two pivot columns, dim Col A =2. Thus, Col A is a two-dimensional subspace of R2, so Col A is equal to R² OC. No, Col A is not R2. Since A has two pivot columns, dim Col A=6. Thus, Col A is equal to R6. O D. No. Since A has two pivot columns, dim Col A = 2. But Col A is a two-dimensional subspace of R5, so Col A is not equal to R². Is Nul A = R62 O A. No, Nul A is not equal to R6. Since A has two pivot columns, dim Nul A = 2. Thus, Nul A is equal to R². B. No, Nul A is not equal to R6. It is true that dim Nul A = 6, but Nul A is a subspace of R³. O C. No, Nul A is equal to R6. Since A has two pivot columns, dim Nul A = 3. Thus, Nul A is equal to R³. OD. Yes, Nul A is equal to R6. Since A has two pivot columns, dim Nul A = 6 Thus, Nul A is equal to R6

Suppose a 5x8 matrix A has two pivot columns. Is Col A =R2? Is Nul A=R6? Explain your answers. Is Col A =R²? OA. No, the column space of A is not R2. Since A has two pivot columns, dim Col A=3. Thus, Col A is equal to R³ OB. Yes. Since A has two pivot columns, dim Col A =2. Thus, Col A is a two-dimensional subspace of R2, so Col A is equal to R² OC. No, Col A is not R2. Since A has two pivot columns, dim Col A=6. Thus, Col A is equal to R6. O D. No. Since A has two pivot columns, dim Col A = 2. But Col A is a two-dimensional subspace of R5, so Col A is not equal to R². Is Nul A = R62 O A. No, Nul A is not equal to R6. Since A has two pivot columns, dim Nul A = 2. Thus, Nul A is equal to R². B. No, Nul A is not equal to R6. It is true that dim Nul A = 6, but Nul A is a subspace of R³. O C. No, Nul A is equal to R6. Since A has two pivot columns, dim Nul A = 3. Thus, Nul A is equal to R³. OD. Yes, Nul A is equal to R6. Since A has two pivot columns, dim Nul A = 6 Thus, Nul A is equal to R6

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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Suppose a 5x8 matrix A has two pivot columns. Is Col A =R2? Is Nul A=R6? Explain your answers. Is Col A =R²? OA. No, the column space of A is not R2. Since A has two pivot columns, dim Col A=3. Thus, Col A is equal to R³ OB. Yes. Since A has two pivot columns, dim Col A =2. Thus, Col A is a two-dimensional subspace of R2, so Col A is equal to R² OC. No, Col A is not R2. Since A has two pivot columns, dim Col A=6. Thus, Col A is equal to R6. O D. No. Since A has two pivot columns, dim Col A = 2. But Col A is a two-dimensional subspace of R5, so Col A is not equal to R². Is Nul A = R62 O A. No, Nul A is not equal to R6. Since A has two pivot columns, dim Nul A = 2. Thus, Nul A is equal to R². B. No, Nul A is not equal to R6. It is true that dim Nul A = 6, but Nul A is a subspace of R³. O C. No, Nul A is equal to R6. Since A has two pivot columns, dim Nul A = 3. Thus, Nul A is equal to R³. OD. Yes, Nul A is equal to R6. Since A has two pivot columns, dim Nul A = 6 Thus, Nul A is equal to R6
Transcribed Image Text:Suppose a 5x8 matrix A has two pivot columns. Is Col A =R2? Is Nul A=R6? Explain your answers. Is Col A =R²? OA. No, the column space of A is not R2. Since A has two pivot columns, dim Col A=3. Thus, Col A is equal to R³ OB. Yes. Since A has two pivot columns, dim Col A =2. Thus, Col A is a two-dimensional subspace of R2, so Col A is equal to R² OC. No, Col A is not R2. Since A has two pivot columns, dim Col A=6. Thus, Col A is equal to R6. O D. No. Since A has two pivot columns, dim Col A = 2. But Col A is a two-dimensional subspace of R5, so Col A is not equal to R². Is Nul A = R62 O A. No, Nul A is not equal to R6. Since A has two pivot columns, dim Nul A = 2. Thus, Nul A is equal to R². B. No, Nul A is not equal to R6. It is true that dim Nul A = 6, but Nul A is a subspace of R³. O C. No, Nul A is equal to R6. Since A has two pivot columns, dim Nul A = 3. Thus, Nul A is equal to R³. OD. Yes, Nul A is equal to R6. Since A has two pivot columns, dim Nul A = 6 Thus, Nul A is equal to R6
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