Consider construction of 2 × 2 real matrix A such that a condition below is satisfied:… 1 answer below »

Consider construction of 2 × 2 real matrix A such that a condition below is satisfied:

(a) Col A = Nul A [0.5]

(b) Nul A = Row A [0.5]

(c) Row A = Col A [0.5]

(d) dim(Col A) = dim(Nul A) [0.3]

(e) dim(Nul A) = dim(Row A) [0.3]

(f) dim(Row A) = dim(Col A) [0.3]

(g) dim(Col A) + dim(Nul A) + dim(Row A) = 2 [0.2]

(h) dim(Col A) + dim(Nul A) + dim(Row A) = 3 [0.2]

(i) dim(Col A) + dim(Nul A) + dim(Row A) = 4 [0.2]

For each sub-question, either provide a proof of impossibility, or an example of possibility.

Where applicable, state also what are dim(Col A), dim(Nul A), and dim(Row A).

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