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andreev551 [17]
2 years ago
15

Determine if the columns of the matrix form a linearly independent set. Justify your answer. Choose the correct answer below. A.

The columns of the matrix do form a linearly independent set because the set contains more vectors than there are entries in each vector. B. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set. C. The columns of the matrix do not form a linearly independent set because the set contains more vectors than there are entries in each vector. D. The columns of the matrix do not form a linearly independent set because there are more entries in each vector than there are vectors in the set.
Mathematics
1 answer:
kondaur [170]2 years ago
4 0

Th matrix is missing. The matrix is :

\begin{bmatrix}1 &-4  &4 \\ -4 &16  & 4 \end{bmatrix}

Solution :

The column of the matrix are \begin{bmatrix}1\\ -4\end{bmatrix} , \begin{bmatrix}-4\\ 16\end{bmatrix}, \begin{bmatrix}4\\ 4\end{bmatrix}

Now each of them are vectors in $IR^2$. But  $IR^2$ has dimensions of 2. But there are 3 column vectors, hence they are linearly dependent.

Therefore, the column of the given matrix does not form the \text{linearly independent set} as the set contains \text{more vectors} than there are entries in each vector.

Therefore, option (D) is correct.

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Answer:

3.2 m

Step-by-step explanation:

Let x be the distance between the cliff and the boat.

Since the cliff is 25 m above sea level and the distance between the boat and the height of the cliff are perpendicular, and the line of sight of the boat to the base of a cliff is 29 , these three form a right-angled triangle with hypotenuse side as the line of sight of the elevation of the boat to the base of the cliff.

So, using trigonometric ratios, tan29° = 25/x

x = 25 m/tan29° = 25 m/0.5543 = 45.1 m

Also, the line of sight of the top of the flagpole, the cliff and the distance between the boat and the cliff form a right-angled triangle with hypotenuse side as the line of sight of the top of the flagpole,

Now, the angle of elevation of the top of the flagpole from the top of the boat is 32°, we now find the angle opposite to x, the distance from the boat to the cliff.  

Since it is a right-angled triangle, thus one angle is 90° and the unknown angle is A.

So, 90° + 32° + A = 180° (sum of angles in a triangle)

122° + A = 180°

A = 180° - 122°

A = 58°

Let y be the length of the flagpole. In this same triangle, using the sine rule, with x being the side opposite A and 25 + y being the side opposite the 32° angle, where 25 + y = height of cliff + length of flagpole, then

x/sinA = (25 + y)/sin32°

25 + y = xsin32°/sinA

y =  xsin32°/sinA - 25

y = 45.1sin32°/sin58° - 25

y = 45.1 × 0.5299/0.8480 - 25

y = 45.1 × 0.6249 - 25

y =28.183 - 25

y = 3.183

y ≅ 3.2 m to one decimal place

6 0
2 years ago
∠A and ∠B are complementary angles. The measure of ∠A=4x° and the measure of ∠B=50°. Find m∠A. * i dont understand can someone h
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Answer:

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Step-by-step explanation:

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10*4 = 40

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Answer:

B. 100

Step-by-step explanation:

This is simple, the picture that is provided tells us the answer easily.

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We are asked to take a look at angle 4, we can see that is more than 90 degrees. Since 100 is the only answer with an amount higher than 90 degrees and fits the angle, it is the angle.

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