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Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 6: Q 6.2-70E (page 293)

Short Answer

Expert verified

Therefore,

Step by step solution

To find the Fibonacci Numbers

Given,

We get,

Therefore, the Fibonacci number was written.

To prove the induction

We will prove this by induction.

To Show that fn+1fn-1-fn2 = (-1)n

We will also prove this by induction.

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Most popular questions from this chapter

Consider two vectors $\overset{鈬赌}{v}$ and $\overset{鈬赌}{w}$ in ${鈩�}^{3}$ . Form the matrix $A = [\overset{鈬赌}{v} x \overset{鈬赌}{w} \overset{鈬赌}{v} \overset{鈬赌}{w}]$ . Express detA in terms of $|| \overset{鈬赌}{v} x \overset{鈬赌}{w} ||$ . For which choices of $\overset{鈬赌}{v}$ and $\overset{鈬赌}{w}$ is Ainvertible?

Find all $2 脳 2$ matrices Asuch that $adj (A) = A^{T}$ .

In an economics text $^{11}$ we find the following system:

$[\begin{matrix} - R_{1} & R_{1} & - (1 - 伪) \\ 伪 & 1 - 伪 & - {(1 - 伪)}^{2} \\ R_{2} & - R_{2} & \frac{- {(1 - 伪)}^{2}}{伪} \end{matrix}] [\begin{matrix} d x_{1} \\ d y_{1} \\ d p \end{matrix}] = [\begin{matrix} 0 \\ 0 \\ - R_{2} d e_{2} \end{matrix}]$ .

Solve for $d x_{1}, d y_{1}$ , and dp. In your answer, you may refer to the determinant of the coefficient matrix as D. (You need not compute D.) The quantities $R_{1}, R_{2}$ and D are positive, and ais between zero and one. If $d e_{2}$ is positive, what can you say about the signs of $d y_{1}$ and dp?

If $A$ is an $n 脳 n$ matrix of rank $n - 1$ , what is the rank of $adj (A)$ ? See Exercises 42 and 43.

(For those who have studied multivariable calculus.) Let Tbe an invertible linear transformation from ${鈩�}^{2}$ to ${鈩�}^{2}$ , represented by the matrix M. Let $惟_{1}$ be the unit square in ${鈩�}^{2}$ and $惟_{2}$ its image under T . Consider a continuous function $f (x, y)$ from ${鈩�}^{2}$ to $鈩�$ , and define the function $g (u, v) = f (T (u, v))$ . What is the relationship between the following two double integrals?

${鈭�}_{惟 2} f (x, y) dA$ and ${鈭�}_{惟 1} g (u, v) dA$

Your answer will involve the matrix M. Hint: What happens when $f (x, y) = 1$ , for all $x, y$ ?

See all solutions

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91影视

Short Answer

Step by step solution

To find the Fibonacci Numbers

To prove the induction

To Show that fn+1fn-1-fn2 = (-1)n

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Most popular questions from this chapter

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