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serg [7]
3 years ago
15

3. Could a 5 x 8 matrix have dim Col A 6 and dim Nul A - 2? Justify your answer. (Hint: Think about the possible pivot rows and

columns
Mathematics
1 answer:
alexdok [17]3 years ago
4 0

Answer:

No

Step-by-step explanation:

A 5x8 matrix A represents a linear transformation between the vector space \mathbb{R}^8 and \mathbb{R}^5. Remeber that the columns of A generate the image of the linear transformation, which is a vector subspace of \mathbb{R}^5. Therefore, \dim \text{Col}A \leq 5, which is the dimension of the the total space.

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