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aleksklad [387]
2 years ago
12

Just need help on first one.​

Mathematics
1 answer:
Nataly [62]2 years ago
7 0

Answer:

1st one because they make less than the actual house

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How to determine if the columns of a matrix are linearly independent?
astra-53 [7]
Let's consider an arbitrary 2x2 matrix as an example,

\mathbf A=\begin{bmatrix}\mathbf x&\mathbf y\end{bmatrix}=\begin{bmatrix}x_1&y_1\\x_2&y_2\end{bmatrix}

The columns of \mathbf A are linearly independent if and only if the column vectors \mathbf x,\mathbf y are linearly independent.

This is the case if the only way we can make a linear combination of \mathbf x,\mathbf y reduce to the zero vector is to multiply the vectors by 0; that is,

c_1\mathbf x+c_2\mathbf y=\mathbf 0

only by letting c_1=c_2=0.

A more concrete example: suppose

\mathbf A=\begin{bmatrix}1&2\\4&8\end{bmatrix}

Here, \mathbf x=\begin{bmatrix}1\\4\end{bmatrix} and \amthbf y=\begin{bmatrix}2\\8\end{bmatrix}. Notice that we can get the zero vector by taking c_1=-2 and c_2=1:

-2\begin{bmatrix}1\\4\end{bmatrix}+\begin{bmatrix}2\\8\end{bmatrix}=\begin{bmatrix}-2+2\\-8+8\end{bmatrix}=\mathbf 0

so the columns of \mathbf A are not linearly independent, or linearly dependent.
8 0
2 years ago
The area of a rectangle is 12.65 m^2. the length measures 5.5 m. what is the width of the rectangle?
Nat2105 [25]

Answer:

The width of the rectangle is 2.3 m

Step-by-step explanation:

Now, when we are asked to find the area of the rectangle, we will use the formula: Area= length * width. We should be given with at least two values, and then we can use the above formula and can find the third variable.

Now, we are given that the area of a rectangle is 12.65 m^2 and the length measures 5.5 m

So the width is given as:

Area= length * width\\\Rightarrow 12.56= 5.5 * width\\\Rightarrow width= \frac{12.56}{5.5}\\\Rightarrow width=2.3 ~m

So this is the required with of the rectangle.

4 0
3 years ago
Read 2 more answers
Help please :D :D :D
SVEN [57.7K]

Hey there!

I'm thinking B because it just makes the most sense reading it aloud. Quick tip though when there's a question like this just read the paragraph or sentences with all the possibilities in the blanks and you can kind of just tell which one it is by the way it sounds, you know?

Hope I helped, lemme know if I'm correct please! Have a spectacular day!

5 0
3 years ago
Two numbers less than 8 that<br> have 3 as their GCF
Anarel [89]

Answer:

3 and 6

Step-by-step explanation:

GCF's or greatest common factors of numbers 1 to 8

1 : 1

2 : 1, 2

3: 1 , 3

4 : 1, 2, 4

5 : 1, 5

6 : 1, 2, 3, 6

7 : 1, 7

8 : 1, 2, 4, 8

3 and 6 have 3 as their GCF

4 0
2 years ago
What is the first digit quotient for 18.6<br><br><br> Please respond ASAP
NISA [10]
I don’t know sorry I’m on the same one and can’t find it out
7 0
2 years ago
Read 2 more answers
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