Answer:
7
Step-by-step explanation:
3 + m =
3 + 4 =
7
9514 1404 393
Answer:
-2x +4
Step-by-step explanation:
We can write the polynomial p(x) in terms of the factors (x+2) and (x-3) as ...
p(x) = (x+2)(x-3)q(x) +ax +b
Where ax+b is the remainder from division by x^2 -x -6 = (x+2)(x-3). The values of 'a' and 'b' can be found from ...
p(-2) = 8 = -2a +b
p(3) = -2 = 3a +b
Subtracting the first equation from the second gives ...
(3a +b) -(-2a +b) = (-2) -(8)
5a = -10
a = -2
Then the first equation tells us ...
8 = -2(-2) +b
4 = b
So, the remainder from division by (x^2 -x -6) is (-2x +4).
Answer:

Step-by-step explanation:
![x^2 > 100\\\\\mathrm{For\:}u^n\:>\:a\\\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\:\:\sqrt[n]{a}\\\\x\sqrt{100}\\\\\sqrt{100}=10\\\\x10](https://tex.z-dn.net/?f=x%5E2%20%3E%20100%5C%5C%5C%5C%5Cmathrm%7BFor%5C%3A%7Du%5En%5C%3A%3E%5C%3Aa%5C%5C%5Cmathrm%7B%2C%5C%3Aif%5C%3A%7Dn%5C%3A%5Cmathrm%7Bis%5C%3Aeven%7D%5Cmathrm%7B%5C%3Athen%5C%3A%7Du%5C%3A%3C%5C%3A-%5Csqrt%5Bn%5D%7Ba%7D%5C%3Aor%5C%3Au%5C%3A%3E%5C%3A%5Csqrt%5Bn%5D%7Ba%7D%5C%5C%5C%5Cx%3C-%5Csqrt%7B100%7D%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax%3E%5Csqrt%7B100%7D%5C%5C%5C%5C%5Csqrt%7B100%7D%3D10%5C%5C%5C%5Cx%3C-10%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax%3E10)
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]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%260%261%5C%5C2%26-4%262%5C%5C-3%26-2%261%5Cend%7Barray%7D%5Cright%5D)
to find the eigenvalues of the matrix you use the following:

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]](https://tex.z-dn.net/?f=A-%5Clambda%20I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3-%5Clambda%260%261%5C%5C2%26-4-%5Clambda%262%5C%5C-3%26-2%261-%5Clambda%5Cend%7Barray%7D%5Cright%5D)
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](https://tex.z-dn.net/?f=%5B%28-3-%5Clambda%29%28-4-%5Clambda%29%281-%5Clambda%29%2B%280%29%282%29%28-3%29%2B%282%29%28-2%29%281%29%5D-%5B%281%29%28-4-%5Clambda%29%28-3%29%2B%280%29%282%29%281-%5Clambda%29%2B%282%29%28-2%29%28-3-%5Clambda%29%5D%3D0%5C%5C%5C%5C-%5Clambda%5E3-6%5Clambda%5E2-12%5Clambda-16%3D0)
and the roots of this polynomial is:

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)
1,081,620
2 x 2 is 4
9 x 30045 is 270,405
so 4 x 270,405 is 1,081,620