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Let A be an m × n matrix and B be an m × p...

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Advance Math

Let A be an m × n matrix and B be an m × p matrix. Let C =[A |B] be an m×(n + p) matrix.

(a) Show that R(C) = R(A) + R(B), where R(·) denotes the rangeof a matrix.

(b) Show that rank(C) = rank(A) + rank(B)−dim(R(A)∩R(B)).

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