Answer:
Step-by-step explanation:
We have to diagonalize the matrix
![\left[\begin{array}{ccc}1&-1&0\\5&1&4\\0&1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-1%260%5C%5C5%261%264%5C%5C0%261%261%5Cend%7Barray%7D%5Cright%5D)
we have to solve the expression
![|A-\lambda I|=0](https://tex.z-dn.net/?f=%7CA-%5Clambda%20I%7C%3D0)
Thus, by applying the determinant we obtain the polynomial
![(1-\lambda )^3+5-4=0\\(1-\lambda )^3+1=0\\](https://tex.z-dn.net/?f=%281-%5Clambda%20%29%5E3%2B5-4%3D0%5C%5C%281-%5Clambda%20%29%5E3%2B1%3D0%5C%5C)
![-\lambda^3+3\lambda^2-4\lambda+2](https://tex.z-dn.net/?f=-%5Clambda%5E3%2B3%5Clambda%5E2-4%5Clambda%2B2)
![\lambda_1=1\\\lambda_2=1-i\\\lambda_3=1+i\\](https://tex.z-dn.net/?f=%5Clambda_1%3D1%5C%5C%5Clambda_2%3D1-i%5C%5C%5Clambda_3%3D1%2Bi%5C%5C)
and the eigenvector will be
![v_1=(-4,0,5)\\v_2=(-1,-i,-1)\\v_3=(-1,i,1)](https://tex.z-dn.net/?f=v_1%3D%28-4%2C0%2C5%29%5C%5Cv_2%3D%28-1%2C-i%2C-1%29%5C%5Cv_3%3D%28-1%2Ci%2C1%29)
HOPE THIS HELPS!!
There are 9 cans of soup and 5 cans of frozen dinner.
The variables used for soup and frozen dinner are x and y respectively.
Step-by-step explanation:
Let,
Soup = x
Frozen Dinner = y
According to given statement of sodium;
300x + 500y = 5200 eqn 1
And,
x + y = 14 eqn 2
![Multiplying\ equation\ 2\ with\ 300\\300(x+y=14)\\300x+300y=4200\ Eqn 3\\](https://tex.z-dn.net/?f=Multiplying%5C%20equation%5C%202%5C%20with%5C%20300%5C%5C300%28x%2By%3D14%29%5C%5C300x%2B300y%3D4200%5C%20Eqn%203%5C%5C)
Subtracting Eqn 3 from Eqn 1;
![(300x+500y)-(300x+300y)=5200-4200\\300x+500y-300x-300y=1000\\200y=1000\\y=\frac{1000}{200} \\y=5](https://tex.z-dn.net/?f=%28300x%2B500y%29-%28300x%2B300y%29%3D5200-4200%5C%5C300x%2B500y-300x-300y%3D1000%5C%5C200y%3D1000%5C%5Cy%3D%5Cfrac%7B1000%7D%7B200%7D%20%5C%5Cy%3D5)
Putting value of y in Eqn 1;
![300x+500(5)=5200\\300x+2500=5200\\\\Subtracting\ 2500\ from\ both\ sides\ \\300x+2500-2500=5200-2500\\300x=2700\\x=\frac{2700}{300} \\x=9](https://tex.z-dn.net/?f=300x%2B500%285%29%3D5200%5C%5C300x%2B2500%3D5200%5C%5C%5C%5CSubtracting%5C%202500%5C%20from%5C%20both%5C%20sides%5C%20%5C%5C300x%2B2500-2500%3D5200-2500%5C%5C300x%3D2700%5C%5Cx%3D%5Cfrac%7B2700%7D%7B300%7D%20%5C%5Cx%3D9)
There are 9 cans of soup and 5 cans of frozen dinner.
The variables used for soup and frozen dinner are x and y respectively.
Keywords: Variables, linear equations, subtraction.
Learn more about linear equations at;
#LearnwithBrainly
C (1,8) and (4,5). To interpret a system of equations when shown a graph, look for the points at which the two function intersect or meet. in this case they meet at both points (1,8) and (4,5)
Let the number be x.
then the number is (x + 6)
the difference between their squares is 192
(x + 6)² - x² = 192
expanding we get;
x² + 12x + 36 - x² = 192
12x + 36 = 192
12x = 192 - 36
12x = 156
x = 13
the numbers are 13 and 19.
hope this helps, God bless!
33, 21,49
Are all composite numbers. :)