Problem

Find the rank of the matrix A=[123 456 789]

Answer

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Answer

This is the RREF of matrix A. The rank of a matrix is the maximum number of linearly independent rows, which in this case is 2.

Steps

Step 1 ：First, we perform Gaussian elimination on matrix A to put it in row-reduced echelon form (RREF).

Step 2 ：Subtract 4 times the first row from the second, and 7 times the first row from the third. This gives us [123 0−3−6 0−6−12].

Step 3 ：Next, divide the second row by -3, and add 2 times the second row to the third. This gives us [123 012 000].

Step 4 ：This is the RREF of matrix A. The rank of a matrix is the maximum number of linearly independent rows, which in this case is 2.

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