Determine whether the following matrices are equivalent or not? Give justification.

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1 Answer
Feb 25, 2018

The two matrices are row equivalent.

Explanation:

Two matrices are row equivalent if there are a series of elementary row operations by which one can be converted to another.

Now, both of the matrices are non-singular #3times 3# matrices (as is easily checked, both have a determinant #=6 ne 0#) , they are both row equivalent to the #3 times 3 identity matrix. (the elementary row operations that are needed to show this are precisely the ones that are carried out in Gauss-Jordan elimination.

Since row equivalence is transitive, they must be row equivalent themselves.

Explicitly showing that the matrix #B# can be obtained from #A# is a bit messy (and unnecessary to answer this question. If desired, we can always first apply the row operations that reduces #A# to #I_3# and then apply the corresponding operations for #B# in reverse order.