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Chapter 1: Q46E (page 36)

Find the rank of the matrix

[abc0de00f],

where a, d and f are nonzero, and b,c and e are arbitrary numbers.

Short Answer

Expert verified

The rank of the matrix abc0de00fis, 3.

Step by step solution

01

Consider the systems

The number of leading 1鈥檚 inrref(A)represents the rank of a matrix Adenoted byrank(A).

Consider the matrix,

abc0de00f

02

Determine the rank of a matrix

The matrix abc0de00f,is already in its reduced row-echelon form with the upper triangular matrix.

As a,d,fare non-zero, can be considered as 1鈥檚.

Hence, 3 is the rank of the matrixabc0de00f.

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