In Exercises 1–28, compute the products. Some of these may be undefined. Exercises marked should be done by using technology. The others should be done in two ways: by hand and by using technology where possible. [ HINT: See Example 3.] [ 1 0 − 1 2 − 2 1 0 0 1 ] [ 1 − 1 4 1 1 0 0 4 1 ]
In Exercises 1–28, compute the products. Some of these may be undefined. Exercises marked should be done by using technology. The others should be done in two ways: by hand and by using technology where possible. [ HINT: See Example 3.] [ 1 0 − 1 2 − 2 1 0 0 1 ] [ 1 − 1 4 1 1 0 0 4 1 ]
Solution Summary: The author calculates the product of the matrices left[cc1& -1 2&
In Exercises 1–28, compute the products. Some of these may be undefined. Exercises marked should be done by using technology. The others should be done in two ways: by hand and by using technology where possible. [HINT: See Example 3.]
Classify the quadratic forms in Exercises 9–18. Then make a
change of variable, x = Py, that transforms the quadratic form
into one with no cross-product term. Write the new quadratic
form. Construct P using the methods of Section 7.1.
11. 2x² + 10x1x2 + 2x3
In Exercises 31–36, find a general formula for f®)(x).
In Exercises 19–22, show there is a number c, with 0 ≤ c ≤ 1, such that f(c) = 0. 19. F(x) = x3 +x2- 1
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