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3 years ago

Is 3/7 and 10/21 proportional ? 15 points

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

4 0

Answer:

NOT proportional.

Step-by-step explanation:

Get a common denominator of 21 by multiplying 7 and 3 by 3.

$\frac{3}{7}(\frac{3}{3})=\frac{9}{21}$

When both fractions have the same denominator, their numerators are different. Therefore, they are NOT proportional.

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3 years ago

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Answer:

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2 years ago

How many times does eight go into 20

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3 years ago

If you have 3/4 cup of flour how many eigths do you have

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3 years ago

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of th

Aliun [14]

Answer:

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

$A=\left[\begin{array}{ccc}-3&0&1\\2&-4&2\\-3&-2&1\end{array}\right]$

to find the eigenvalues of the matrix you use the following:

$det(A-\lambda I)=0$

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

$A-\lambda I=\left[\begin{array}{ccc}-3-\lambda&0&1\\2&-4-\lambda&2\\-3&-2&1-\lambda\end{array}\right]$

and by taking the determinant:

$[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-\lambda)+(2)(-2)(-3-\lambda)]=0\\\\-\lambda^3-6\lambda^2-12\lambda-16=0$

and the roots of this polynomial is:

$\lambda_1=-4\\\\\lambda_2=-1+i\sqrt{3}\\\\\lambda_3=-1-i\sqrt{3}$

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

3 0

3 years ago