27.5. EXERCISES 517
8. Find the determinant using row operations.∣∣∣∣∣∣∣∣∣1 2 1 23 1 −2 3−1 0 3 12 3 2 −2
∣∣∣∣∣∣∣∣∣9. Find the determinant using row operations.∣∣∣∣∣∣∣∣∣
1 4 1 23 2 −2 3−1 0 3 32 1 2 −2
∣∣∣∣∣∣∣∣∣10. Verify an example of each property of determinants found in Theorems 27.1.23 -
27.1.25 for 2×2 matrices.
11. An operation is done to get from the first matrix to the second. Identify what wasdone and tell how it will affect the value of the determinant.(
a bc d
),
(a cb d
)
12. An operation is done to get from the first matrix to the second. Identify what wasdone and tell how it will affect the value of the determinant.(
a bc d
),
(c da b
)
13. An operation is done to get from the first matrix to the second. Identify what wasdone and tell how it will affect the value of the determinant.(
a bc d
),
(a b
a+ c b+d
)
14. An operation is done to get from the first matrix to the second. Identify what wasdone and tell how it will affect the value of the determinant.(
a bc d
),
(a b2c 2d
)
15. An operation is done to get from the first matrix to the second. Identify what wasdone and tell how it will affect the value of the determinant.(
a bc d
),
(b ad c
)