Question: Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary. Wequals=StartSet

Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.

Wequals=StartSet left bracket Start 4 By 1 Matrix 1st Row 1st Column p 2nd Row 1st Column q 3rd Row 1st Column r 4st Row 1st Column s EndMatrix right bracket : Start 2 By 1 Matrix 1st Row 1st Column p plus 3 q equals negative 2 s 2nd Row 1st Column negative 3 p equals 2 s minus r EndMatrix EndSet

p+3q=2s

3p=2sr

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Part 1

Rewrite the system of equations in the form

Axequals=0.

Axequals=left bracket Start 2 By 4 Matrix 1st Row 1st Column 1 2nd Column 3 3rd Column 0 4st Column nothing 2nd Row 1st Column negative 3 2nd Column 0 3rd Column nothing 4st Column nothing EndMatrix right bracket

11	3	0	enter your response here
3	0	enter your response here	enter your response here

left bracket Start 4 By 1 Matrix 1st Row 1st Column p 2nd Row 1st Column q 3rd Row 1st Column r 4st Row 1st Column s EndMatrix right bracket

equals=left bracket Start 2 By 1 Matrix 1st Row 1st Column 0 2nd Row 1st Column 0 EndMatrix right bracket

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