BUSINESS ADMINISTRATION
BUSINESS MATHEMATICS
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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The rank of m X n matrix whose elements are unity is ____
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0
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1
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m
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n
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Explanation:
Detailed explanation-1: -Matrix A has only one linearly independent row, so its rank is 1.
Detailed explanation-2: -A square matrix where every element is unity is called as identity matrix.
Detailed explanation-3: -Note: In any non-zero matrix, if all rows or all columns are same, then the rank of that matrix will always be 1.
Detailed explanation-4: -The rank of a matrix is the dimension of the subspace spanned by its rows. As we will prove in Chapter 15, the dimension of the column space is equal to the rank. This has important consequences; for instance, if A is an m × n matrix and m ≥ n, then rank (A) ≤ n, but if m < n, then rank (A) ≤ m.
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