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Vlada [557]
3 years ago
9

PLEASE HELP! find the inverse matrix​

Mathematics
2 answers:
nikitadnepr [17]3 years ago
5 0

Answer:

Step-by-step explanation:

A=\begin{bmatrix}11&-5\\3&-1\end{bmatrix}\\det(A)=11*(-1)-3*(-5)=-11+15=4\\minor=\begin{bmatrix}-1&3\\-5&11\end{bmatrix}\\cofactor=\begin{bmatrix}-1&-3\\5&11\end{bmatrix}\\Transposed\ cofactor=\begin{bmatrix}-1&5\\-3&11\end{bmatrix}\\A^{-1}=\dfrac{Transposed\ cofactorx}{det(A)} =\begin{bmatrix}\dfrac{-1}{4} &\dfrac{5}{4} \\\\ \dfrac{-3}{4} &\dfrac{11}{4}\end{bmatrix}\\

Proof:\\A*A^{-1}=\begin{bmatrix}11&-5\\\\3&-1\end{bmatrix}*\begin{bmatrix}\dfrac{-1}{4} &\dfrac{5}{4}\\\\ \dfrac{-3}{4}&\dfrac{11}{4}\end{bmatrix}\\\\\\=\begin{bmatrix}\dfrac{-11+15}{4} &\dfrac{55-55}{4}\\\\ \dfrac{-3+3}{4}&\dfrac{15-11}{4}\end{bmatrix}\\\\\\=\begin{bmatrix}1&0\\\\ 0&1\end{bmatrix}\\

Bonus: method of Gauss 's pivot jointed

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Sauron [17]3 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

The inverse of a matrix A = \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] is

A^{-1} = \frac{1}{ad-bc} \left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]

If ad - bc = 0 then the matrix has no inverse

A = \left[\begin{array}{ccc}11&-5\\3&-1\\\end{array}\right]

ad - bc = (11 × - 1) - (- 5 × 3) = - 11 - (- 15) = - 11 + 15 = 4 , then

A^{-1} = \frac{1}{4} \left[\begin{array}{ccc}-1&3\\-5&11\\\end{array}\right] = \left[\begin{array}{ccc}-0.25&0.75\\-1.25&2.75\\\end{array}\right]

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Answer:

(0,1)

Step-by-step explanation:

The solution to a system of equations is where the two lines intersect. Algebraically, you could solve this by setting the equations equal to each other.

I hope this helps!

7 0
4 years ago
Which equation represents the graph<br><br>A. y=x-2<br><br>B.y=x+2<br><br>C.y=1/2x<br><br>D.y=2x​
cluponka [151]

x=0, y=0

x=3, y=6

This means: y=2x

Answer: D)

6 0
3 years ago
Select the correct answer.
alexandr1967 [171]

Answer:

4 is the answer

Step-by-step explanation:

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5 0
2 years ago
Read 2 more answers
Geometry question 2, Thanks if you help!
wlad13 [49]
A. 113 because vertical angles are congruent.
8 0
3 years ago
Write an equation in point slope from for the line through the given point which the given slope
shusha [124]

   The equation in point slope is y-3=6(x-8) which is mentioned in option C If the line through the given point which the given slope (8,3), m=6.

Step-by-step explanation:

The given is,

                   The point - ( 8,3 )

                    Slope, m = 6

Step:1

          Formula for slope of line is,

                                Slope,m=\frac{y_{2}-y_{1}  } {x_{2}- x_{1}  } ..................(1)

          Here,  (x_{1} ,y_{1} ) and  (x_{2} ,y_{2} ) are points and slope (m)

Step:2

          From given,

                               (x_{1} ,y_{1} ) - (8, 3)

                               (x_{2} ,y_{2} ) - (x, y)

         Substitute the values of points and slope in  the equation (1),

                                         6=\frac{y-8  } {x- 3  }

         Take ({x- 8  }) in left side,

                              6(x-3)=(y-3)

                               (y-3)=6(x-3)

Result:

           The equation in point slope is y-3=6(x-8) which is mentioned in option C If the line through the given point which the given slope (8,3), m=6.

                                       

8 0
3 years ago
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