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Sagot :
The required elementary matrix E such that EA = B is
[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].
Any matrix obtained by performing a single elementary row operation on the identity matrix is called an elementary matrix.
The elementary operations are as follows:
1. Interchange the two rows of a matrix
2. Multiply a row of a matrix by the non-zero scalar k.
3. Add k-times of a row into another row of the matrix.
Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.To perform an elementary row operation on A, an n×m matrix, take the following steps:
1. To find E, the elementary row operator, apply the operation to an n×n identity matrix.
2. To carry out the elementary row operation, premultiply A by E.
We want to interchange the first and second rows of A, a 3×3 matrix to get B. To create the elementary row operator E, we interchange the first and second rows of the identity matrix I3:
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex] is changed to [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].
So, [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex][tex]\left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right][/tex]
Thus, the required elementary matrix E such that EA = B is
[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]
To learn more about elementary matrix, visit: brainly.com/question/29024055
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