In each part, find the largest possible value for the rank of \( A \) and the smallest possible value for the nullity of \( A \), assuming \( A \) has the indicated order (size). (i) \( 4 \times 5 \) Rank is Nullity is (ii) \( 8 \times 5 \) Rank is Nullity is (iii) \( 5 \times 7 \) Rank is Nullity is
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The nullity of a matrix is the dimension of its null space, which is the number of free variables in the system of linear equations represented by the matrix. Since the matrix has 5 columns, the smallest possible nullity is 5 - 4 = 1. Show more…
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