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djverab [1.8K]
3 years ago
5

Determine which of the indicated column vectors are eigenvectors of the given matrix

Mathematics
1 answer:
gladu [14]3 years ago
7 0
]Eigenvectors are found by the equation (A-\lambda I) \vec{v} = 0$ implying that \det(A-\lambda I) = 0. We then can write:

A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ] 

And:

\det(A-\lambda I) = (4-\lambda)(1-\lambda) - 10 = 0 

Gives us the characteristic polynomial:

\lambda^2 - 5 \lambda -6 = 0 \implies \lambda_1 = -1, \lambda_2 = 6

So, solving for each eigenvector subspace:

\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]

Gives us the system of equations:

4x + 2y = -x \newline 5x + y = - y 

Producing the subspace along the line y = -\frac{5}{2} x

We can see then that 3 is the answer. 



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Add (7х2 – 3x) + (5х – 6).
Masja [62]

Option C: The solution is 7x^{2} +2x-6

Explanation:

The given expression is (7x^{2} -3x)+(5x-6)

We need to solution of the given expression.

The solution of the given expression can be determined by adding the two expressions.

Let us remove the parenthesis.

Thus, we have,

7x^{2} -3x+5x-6

Adding the like terms, we have,

7x^{2} +2x-6

Thus, the solution is 7x^{2} +2x-6

Hence, Option C is the correct answer.

5 0
3 years ago
Raziel walks 3 m north, 5 m east, 3 m south, and 5 m west. What is the total distance Raziel traveled? (Include
blsea [12.9K]

Answer:

16 metres

Step-by-step explanation:

You're finding the perimetre of this rectangle, so have to add each side together to find the total distance he traveled (the perimetre of the rectangle, since he travelled in a rectangle).

3*2 is 6,

5*2 is 10

10 + 6 is 16.

Have a wonderful day, my friend.

4 0
3 years ago
The hardware store where you work charge 80 cents including tax, for a pound of nails. A customer purchases 5 3/4 pound of nails
Sophie [7]

Answer:

$4.60

Step-by-step explanation:

1 lb ---> 80 cents

5 3/4 lb ---> 5 3/4 * 80 cents

5 \dfrac{3}{4} \times 80 =

= \dfrac{23}{4} \times \dfrac{80}{1}

= \dfrac{23 \times 80}{4 \times 1}

= \dfrac{1840}{4}

= 460

460 cents = $4.60

5 0
2 years ago
Read 2 more answers
How does the volume of a sphere compare to that of the volume of a cylinder? What would you say the scale factor for Vol sphere:
borishaifa [10]

Answer:

The volume of a sphere is 2/3 times the volume of a similar cylinder

Scale factor : 2/3

Step-by-step explanation:

Let us consider a sphere of radius r. The volume of the sphere will be given as

V_{s}=\frac{4}{3} \pi r^{3}

Similarly, let us consider a cylinder with its height being twice the radius of the sphere. We will have its volume given as:

V_{c}=\pi r^{2}h

but h = 2r

Hence we have

V_{c}= 2\pi r^{3}h

We can divide the two volumes to get a constant that links them together

\frac{V_{s}}{V_{c}}=\frac{\frac{4}{3} \pi r^{3}}{2\pi r^{3}h}

this will give us 2/3

Hence the scale factor for Vol sphere: Vol cylinder is 2/3

3 0
3 years ago
Fiona joins a fruit of the month club. The entry cost is $25 and then she pays $18 per month. If she participates for 8 months,
xeze [42]

Answer: $169

Step-by-step explanation: The expression 25 + 18 x 8 represents the amount she will pay if she participates for 8 months.

Multiply 18 x 8 to find the cost for 8 months. $18 x 8 = $144.

Now add $25 to $144, which equals $169

5 0
3 years ago
Read 2 more answers
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