For each of the following row operations, write the 5 x 5elementary matrix that

Question

For each of the following row operations, write the 5 x 5elementary matrix that performs that operation by leftmultiplication. Write down the elementary matrix which undos ( theinverse) these operations.
i. exchange row 2 and row 3 ii. multiplying row 2 by -4 iii. Add 2 times row 1 to row 5.
(b) Consider the matrix
___ ___ | 1 -6 6 1 | | 0 -2 -2 1 | | 0 2 1 -2 |   = A | 0 6 0 5 | |___ ___| Find a matrix E which makes the second pivot 1 and zero outsthe entries below and above it that is, find an matrix E sothat (EA)*2=0    1    0    0    


i. exchange row 2 and row 3 ii. multiplying row 2 by -4 iii. Add 2 times row 1 to row 5.
(b) Consider the matrix
___ ___ | 1 -6 6 1 | | 0 -2 -2 1 | | 0 2 1 -2 |   = A | 0 6 0 5 | |___ ___| Find a matrix E which makes the second pivot 1 and zero outsthe entries below and above it that is, find an matrix E sothat (EA)*2=0    1    0    0    

Explanation / Answer

UNIT MATRIX = I5 = 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 i. exchange row 2 and row 3
ELEMENTARY MATRIX FORH23= EXCHAGE ROWS 2 AND 3 IN I5 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1

ii. multiplying row 2 by -4
ELEMENTARY MATRIX FORH2(-4)= MULTIPLY ROW 2 IN I5 WITH -4 1 0 0 0 0 0 -4 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
iii. Add 2 times row 1 to row 5.
ELEMENTARY MATRIX FORH51(2)= ADD 2 TIMES ROW 1 TO ROW 5 IN I5 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 2 0 0 0 1
UNIT MATRIX = I5 = 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1

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