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Marizza181 [45]

4 years ago

10

In a restaurant john bought one cup of gumbo and two salads for $12.25. Greg bought 4 gumbos and 4 salads for $31 how much does

each cup of gumbo and salad cost.

1 answer:

Sever21 [200]4 years ago

7 0

The answer is some number

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Consider the matrix A. A = 1 0 1 1 0 0 0 0 0 Find the characteristic polynomial for the matrix A. (Write your answer in terms of

dusya [7]

Answer with Step-by-step explanation:

We are given that a matrix

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

a.We have to find characteristic polynomial in terms of A

We know that characteristic equation of given matrix $\mid{A-\lambda I}\mid=0$

Where I is identity matrix of the order of given matrix

I= $\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

Substitute the values then, we get

$\begin{vmatrix}1-\lambda&0&1\\1&-\lambda&0\\0&0&-\lambda\end{vmatrix}=0$

$(1-\lambda)(\lamda^2)-0+0=0$

$\lambda^2-\lambda^3=0$

$\lambda^3-\lambda^2=0$

Hence, characteristic polynomial = $\lambda^3-\lambda^2=0$

b.We have to find the eigen value for given matrix

$\lambda^2(1-\lambda)=0$

Then , we get $\lambda=0,0,1-\lambda=0$

$\lambda=1$

Hence, real eigen values of for the matrix are 0,0 and 1.

c.Eigen space corresponding to eigen value 1 is the null space of matrix $A-I$

$E_1=N(A-I)$

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

Apply $R_1\rightarrow R_1+R_3$

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

Now,(A-I)x=0[/tex]

Substitute the values then we get

$\left[\begin{array}{ccc}0&0&1\\1&-1&0\\0&0&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]=0$

Then , we get $x_3=0$

And $x_1-x_2=0$

$x_1=x_2$

Null space N(A-I) consist of vectors

x= $\left[\begin{array}{ccc}x_1\\x_1\\0\end{array}\right]$

For any scalar $x_1$

$x=x_1\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

$E_1=N(A-I)=Span(\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

Hence, the basis of eigen vector corresponding to eigen value 1 is given by

$\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

Eigen space corresponding to 0 eigen value

$N(A-0I)=\left[\begin{array}{ccc}1&0&1\\1&0&0\\0&0&0\end{array}\right]$

$(A-0I)x=0$

$\left[\begin{array}{ccc}1&0&1\\1&0&0\\0&0&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]=0$

$\left[\begin{array}{ccc}x_1+x_3\\x_1\\0\end{array}\right]=0$

Then, $x_1+x_3=0$

$x_1=0$

Substitute $x_1=0$

Then, we get $x_3=0$

Therefore, the null space consist of vectors

$x=x_2=x_2\left[\begin{array}{ccc}0\\1\\0\end{array}\right]$

Therefore, the basis of eigen space corresponding to eigen value 0 is given by

$\left[\begin{array}{ccc}0\\1\\0\end{array}\right]$

5 0

3 years ago

For which values of P and Q does the following equation have infinitely many solutions

worty [1.4K]

Answer:

hello : P = - 6 and Q = 35

Step-by-step explanation:

Px + 35=-6x + Q

calculate : x

Px + 6x = Q - 35

(P+6) x = Q - 35

this equation have infinitely many solutions if : P+6 = 0 and Q - 35 =0

P = - 6 and Q = 35...( values of P and Q)

5 0

4 years ago

Given h(x)=-x+5, solve for x when h(x)=3. PLEASE I NEED HELP ILL GIVE BRAINLIEST.

Mice21 [21]

$\text{Given that,}\\\\h(x) = -x+5\\\\\implies 3 = -x +5\\\\\implies x = 5 -3 =2$

5 0

3 years ago

HELP NOW II WILL GIVE YOU 30 POINTS

Alex

Answer:

1; -11+ 26 =15

2: 2- (-3) =5

3: 10+ (-4) = 7

4: 11 + -8 =3

5: -2 + 3 =1

6: 8 - 12 = -4

Step-by-step explanation:

!

5 0

3 years ago

How much would $500 invested at 9% interest compounded annually be worth after 4 years? Round your answer to the nearest cent.

frosja888 [35]

A = P(1+(r/n))^nt
A = 500(1+(.09/1))^1<span>∗4
A = 500(1.09)^4
A = 705.79</span>

6 0

3 years ago

Read 2 more answers