thanks Although it seems silly, it is possible to do elementary row operations o

Question

thanks

Although it seems silly, it is possible to do elementary row operations on n x 1 matrices. Every such operation defines a transformation of Rn into Rn. For example, if we define a transformation of R3 into R3 by "add twice row 1 to row 3," this transformation transforms [x1 x2 x3] rightarrow [ x1 x2 x3+2x1] = [ 1 0 0 0 1 0 2 0 1 ] [ x1 x2 x3 ] Since this transformation is described by a matrix, we see that our elementary row operation defines a linear transformation. A transformation defined by a single elementary row operation in called an elementary transformation and the matrix that describes such a transformation is called an elementary matrix. Find matrices that describe the following elementary row operations on Rn for the given value of n. Add twice row 3 to row 2 in R4. Multiply row 2 by 17 in R3. Interchange rows 1 and 2 in R4 .

Explanation / Answer

row transformation of any matrix is equivalent to pre multiplying it by the identity matrix to which those same row transformations have been done

a) [ 1 0 0 0 ]

[ 0 1 2 0 ]

[ 0 0 1 0 ]

[ 0 0 0 1 ]

b) [ 1 0 0 ]

[ 0 17 0 ]

[ 0 0 1 ]

c) [ 0 1 0 0 ]

[ 1 0 0 0 ]

[ 0 0 1 0 ]

[ 0 0 0 1 ]

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