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# sina

• ### Can someone explain this lemma on systems?

I don't understand what is written here.

Mathematics1 month ago

For 4(b).

I think the statement implies the vectors are independent but if you remove one of the vectors, the group of vectors become dependent. But I am not sure. Any help would be much appreciated.

• ### Does S span R^3? ?

For (a), I wrote that the set is linearly dependent as the first two vectors in the set are multiples of each other so it doesn't span R3. It also contains the zero vector. How can I find out the geometric description of each?

Mathematics1 month ago
• ### Which of the three is incorrect?

Which of the three is incorrect and what algebraic step produced this wayward result? What is the full correct result for that particular result of k?

Looking at the rref matrix, I see that (ii) and (iii) are true by plugging in values for k=4 and k=5.

Going back to (i), that must be the untrue statement. But, if you put k=3, the denominator of the last column is undefined.

Mathematics1 month ago
• ### Perform row operations on augmented matrix until critical step is reached?

“You will need to complete all pivoting processes on the first two columns.” I made a start but I am not sure how to get (3,3) =1...