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2 years ago

6

Use the svd() function in MATLAB to compute , the rank-1 approximation of . Clearly state what is, rounded to 4 decimal places.

Also, compute the root mean square error (RMSE) between and .

1 answer:

Afina-wow [57]2 years ago

7 0

Answer:

Here is the Matlab code.

Step-by-step explanation:

Matlab Code:

$A = [1 2 2;3 4 5;6 7 8]\\[U,S,V] = svd(A)u1 = U(:,1)\\u2 = U(:,2)\\u3 = U(:,3)\\d1 = dot(u1,u2)\\c = cross(u1,u2)\\d2 = dot(c,u3)$

$d1 =- 5.5511e-17\\c = -0.7172 0.6643 -0.2103\\d2 = 1$

Yes, since c = cross(u1,u2) is orthogonal to both u1 and u2. Hence is u3, thus the dot product with u3 is 1.

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3 years ago

Is f(x) continuous at x equals 4? Why or why not? A. No, f(x) is not continuous at x equals 4 because ModifyingBelow lim Wit

soldier1979 [14.2K]

<u>Corrected Question</u>

Is the function given by:

$f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right$

continuous at x=4? Why or why not? Choose the correct answer below.

Answer:

(D) Yes, f(x) is continuous at x = 4 because $Lim_{x \to 4}f(x)=f(4)$

Step-by-step explanation:

Given the function:

$f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right$

A function to be continuous at some value c in its domain if the following condition holds:

f(c) exists and is defined.

$Lim_{x \to c}$ f(x)$ exists.

$f(c)=Lim_{x \to c}$ f(x)$

At x=4

$f(4)=\dfrac{1}{4}*4+1=2$

$Lim_{x \to 4}f(x)=2$

Therefore: $Lim_{x \to 4}f(x)=f(4)=2$

By the above, the function satisfies the condition for continuity.

The correct option is D.

3 0

2 years ago

Given g(x)=Squareroot x-4 and h(x)=2x-8, what is g(h(10))

yan [13]

Answer:

$g(h(10)) = 2\sqrt 2$

Step-by-step explanation:

Given

$g(x) = \sqrt {x - 4$

$h(x) = 2x - 8$

Required

$g(h(10))$

First, calculate $g(h(x))$

We have:

$g(x) = \sqrt {x - 4$

This gives:

$g(h(x)) = \sqrt {h(x) - 4$

Substitute $h(x) = 2x - 8$

$g(h(x)) = \sqrt {2x - 8 - 4$

$g(h(x)) = \sqrt {2x - 12$

Substitute $x = 10$

$g(h(10)) = \sqrt {2*10 - 12$

$g(h(10)) = \sqrt {20 - 12$

$g(h(10)) = \sqrt {8\\$

Split

$g(h(10)) = \sqrt {4} * \sqrt 2$

This gives

$g(h(10)) = 2\sqrt 2$

8 0

2 years ago

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