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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