BUSINESS ADMINISTRATION
BUSINESS MATHEMATICS
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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(A) = m (A) < m
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(A) = n
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(A) = min of {m, n}
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(A) < m
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Detailed explanation-1: -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.
Detailed explanation-2: -If A matrix is of order m×n, then (A ) ≤ minm, n = minimum of m, n. If A is of order n×n and |A| ≠ 0, then the rank of A = n. If A is of order n×n and |A| = 0, then the rank of A will be less than n.
Detailed explanation-3: -How to find the rank of matrix? The rank of matrix can be determined by reducing the given matrix in row-reduced echelon form, the number of non-zero rows of the echelon form is equal to the rank of matrix. Rank of matrix can also be calculated by finding order of the highest non-singular minor of the given matrix.
Detailed explanation-4: -The determinant of the 3 × 3 matrix is nonzero; therefore, its rank must be 3.