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Homework 8 Vector spaces and matrices

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[2pts] Prove or give a counterexample: {[x,y,z]:x,y,z∈R,x+y+z+1=1} is a vector space

[2pts] Compute the following matrix vector products:

[■(2&[email protected]&3)]*[■(4&2)]
[■(1&2&[email protected]&1&[email protected]&5&1)]*[■(1&3&2)]

[3pts] Compute the following matrix multiplications:
[■(2&[email protected]&3)][■([email protected])]
[■(1&2&[email protected]&1&[email protected]&5&1)]*[■([email protected]@2)]
[■(1&5&[email protected]&3&2)][■([email protected]@2)]

[3pts] Compute the following matrix multiplications using a transpose:
[■(1&2&[email protected]&1&2)] [■(1&3&2)]^T
[■(1&[email protected]&[email protected]&5)]^T [■(2&0&5)]
[■(1&3&2)] [■(1&3&2)]^T

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