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Math 2318: MLM question 4.2.1 answered two ways.
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(Warning: Really bad hair day in this one...;)
A student asked for an explanation for this MLM question 4.2.1. I took the opportunity to review the definition of Nul()A = Ker(T_A).... but also pointed out you could solve it just by multiplying A by the given w (IF you remembered the definition of Nul(A), of course!). Getting Aw=0 tells you (then) that w does belong to Nul(A). (But what if the question was, "Find Nul(A)????"). That's a hint!
A student asked for an explanation for this MLM question 4.2.1. I took the opportunity to review the definition of Nul()A = Ker(T_A).... but also pointed out you could solve it just by multiplying A by the given w (IF you remembered the definition of Nul(A), of course!). Getting Aw=0 tells you (then) that w does belong to Nul(A). (But what if the question was, "Find Nul(A)????"). That's a hint!