ELEMENTARY MATRICES-2

Reminder: an Elementary Matrix is an Identity matrix
on which a single row operation has been performed.

example: the elementary matrix A = is I 2 x 2 with row 2 added to row 1.

QUESTIONS:

1) Describe in words the row operation indicated by these elementary matrices.

a) b) c) d) e)

f) g) h) i)

2) Write the elementary 2×2 matrix that performs the indicated row operation.

a) row 2 – 5 row 1

b) switch rows 1 and 2

c) row 1 + 4 row 2

d) row 2 + 7 row 1.

3) Write the elementary 3×3 matrix that performs the indicated row operation.

a) row 1 – 3 row 3

b) row 2 + 6 row 1

c) switch rows 1 and 3

d) row 3 – 2 row 1

e) row 3 + 5 row 2.

.

SOLUTIONS:

1)

a) row 1 minus 3 × row 2

b) 7 × row 2

c) row 2 minus 5 × row 1

d) row 1 plus 6 × row 2

e) row 2 minus 4 × row 1

f) row 2 plus 2 × row 1

g) row 3 minus 3 × row 1

h) switch rows 1 and 3

i) row 1 plus 4 × row 3

2)

a) ......... b) ......... c) ......... d) .

3)

a) row 1 – 3 row 3 .................. b) row 2 + 6 row 1

c) switch rows 1 and 3 ..............d) row 3 – 2 row 1

e) row 3 + 5 row 2.

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