Give a 3 × 3 elementary matrix E which will carry out the...

Give a 3 × 3 elementary matrix E which will carry out the row operation R1 ? R2. E = Test that E actually works for carrying out this row operation by computing the product EA for the matrix A = [?3 4 5 4; 1 ?1 ?2 ?3; 3 4 4 2] EA =

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00:01 Hi, we have given matrix a equal to matrix minus 1, minus 3, 8, minus 3, 23, 1, 3 minus 7.

00:18 We need to find a inverse.

00:20 A inverse equal to adjoint of a by determinant of a.

00:26 First we can find the determinant.

00:29 Determinant of a equal to minus 1 into 70 minus 69 plus 3 into 21 minus 23 plus 8 into minus 9 plus 10, that is minus 1 minus 6 plus 8, that is 1.

00:55 So, a inverse equal to adjoined of a by 1, that is a inverse equal to adjoined of a.

01:04 I mean, know that adjoint of a is the transpose of the co -factor matrix.

01:15 So in order to find the co -factor, first we need to find the minus.

01:20 So minor is denoted by small m.

01:23 So m -1 -1 is 1.

01:25 M -1 -2 is minus 2.

01:29 M13, sorry, small m13 equal to 1.

01:32 You know how to calculate the minor right? m11 deleting this row and this column and multiplying, finding the determinant of this 2 by 2 matrix, that will be m11.

01:46 M12 deleting this column and row, then find matrix 3 minus 3 into 7 minus 1 into 23 like that.

01:56 Okay.

01:58 Then m2 .1 equal to 21 minus 24, that is minus 3.

02:04 M22 equal to minus 1.

02:07 M23 equal to 0.

02:11 M31 equal to 1.

02:13 M32 is minus 23 plus 24.

02:17 That is 1...

Question

Give a 3 × 3 elementary matrix E which will carry out the row operation R1 ? R2. E = Test that E actually works for carrying out this row operation by computing the product EA for the matrix A = [?3 4 5 4; 1 ?1 ?2 ?3; 3 4 4 2] EA =

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