X2 – 1x – 90 = 0 has solutions {a, b}. What is a + b?

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

3 0

Answer:

a + b =1

Step-by-step explanation:

Write the given quadratic as x^2 – 1x – 90 = 0. This factors into

(x - 10)(x + 9) = 0, and so the roots/solutions are {-9, 10}.

If we call -9 "a" and 10 "b," then the sum a + b is -9 + 10, or a + b =1.

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16. Let W be the set of all vectors in R3 of the form a+2b b -3a Find a basis for Wand state the dimension of W.

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$W=\{\left[\begin{array}{ccc}a+2b\\b\\-3a\end{array}\right]: a,b\in\mathbb{R} \}$

Observe that if the vector $x=\left[\begin{array}{ccc}x\\y\\z\end{array}\right]$ is in W then it satisfies:

$\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{c}a+2b\\b\\-3a\end{array}\right]=a\left[\begin{array}{c}1\\0\\-3\end{array}\right]+b\left[\begin{array}{c}2\\1\\0\end{array}\right]$

This means that each vector in W can be expressed as a linear combination of the vectors $\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]$