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3 years ago

Evaluate the expression below. a = -8, b = - 4.1, and c = 9.

Mathematics

1 answer:

wolverine [178]3 years ago

5 0

Answer:

-9+(-4.1)-(-8)

= -9-4.1+8

= -5.1

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Find a formula for the least squares solution of ax=b when the columns of a are orthonormal1 .

neonofarm [45]

Let $\mathbf A$ be a rectangular $m\times n$ matrix with column vectors $\mathbf a_1,\ldots,\mathbf a_n$ , i.e.

$\mathbf A=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}$

Then we have

$\mathbf A^\top=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}^\top$

and the product of the two is

$\mathbf A^\top\mathbf A=\begin{bmatrix}\mathbf a_1\cdot\mathbf a_1&\mathbf a_1\cdot\mathbf a_2&\cdots&\mathbf a_1\cdot\mathbf a_n\\\mathbf a_2\cdot\mathbf a_1&\mathbf a_2\cdot\mathbf a_2&\cdots&\mathbf a_2\cdot\mathbf a_n\\\vdots&\vdots&\ddots&\vdots\\\mathbf a_n\cdot\mathbf a_1&\mathbf a_n\cdot\mathbf a_2&\cdots&\mathbf a_n\cdot\mathbf a_n\end{bmatrix}$

Because the columns of $\mathbf A$ are orthonormal, we have

$\mathbf a_i\cdot\mathbf a_j=\begin{cases}1&\text{for }i=j\\0&\text{for }i\neq j\end{cases}$

which means $\mathbf A^\top\mathbf A$ reduces to an $n\times n$ matrix with ones along the diagonal and zero everywhere else, i.e.

$\mathbf A^\top\mathbf A=\begin{bmatrix}1&0&\cdots&0\\0&1&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&0&\cdots&1\end{bmatrix}=\mathbf I_n$

where $\mathbf I$ denotes the identity matrix. This means the solution to $\mathbf{Ax}=\mathbf b$ is given by

$\mathbf A^\top(\mathbf{Ax})=\mathbf A^\top\mathbf b\implies(\underbrace{\mathbf A^\top\mathbf A}_{\mathbf I})\mathbf x=\mathbf A^\top\mathbf b\implies\mathbf x=\mathbf A^\top\mathbf b$

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3 years ago

Need answer fast u better give it to me i love u

Basile [38]

Answer:

B) A = 2x² - 8x + 8

Step-by-step explanation:

Area of a triangle

A = 1/2bh

Here,

b = 2x - 4
h = 2x - 4

Solving

A = 1/2 (2x - 4) (2x - 4)
A = 1/2 (2x - 4)²
A = 1/2 (4x² - 16x + 16)
A = 2x² - 8x + 8

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3 years ago

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What is the value of 10C3? A. 30 B.120 C.720 D.1000

sergij07 [2.7K]

The correct answer is B. 120

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3 years ago

Somebody please help me. This makes zero sense.

earnstyle [38]

Answer:

Step-by-step explanation:

rearrange it like an equation.

take everything else out of the middle apart from x.

make sure that what you do to the middle you do to both sides

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3 years ago

Savannah measure's the temperature of a liquid to be 24 Celsius. Convert to Fahrenheit

jek_recluse [69]

Answer:

The temperature of Savannah's liquid to the nearest degree Fahrenheit is 75.2.

Step-by-step explanation:

The general formula to convert celsius into fahrenheit is

F=(C*9/5)+32

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F= 43.2 +32

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Therefore, The temperature of Savannah's liquid to the nearest degree Fahrenheit is 75.2

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4 years ago

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