The inverse of the matrix ![\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D11%26-5%5C%5C3%26-1%5Cend%7Barray%7D%5Cright%5D)
is the matrix ![\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B-1%7D%7B4%7D%20%26%5Cfrac%7B5%7D%7B4%7D%20%5C%5C%5C%5C%5Cfrac%7B-3%7D%7B4%7D%20%26%5Cfrac%7B11%7D%7B4%7D%20%5Cend%7Barray%7D%5Cright%5D)
.
The inverse of a matrix A is calculated by the formula:
A' = (1/|A|)(Adj A),
where A' represents the inverse of matrix A,
|A| represents the determinant value of matrix A, and
Adj A represents the Adjoin matrix of matrix A.
So, to calculate the inverse of the matrix , we will first calculate its Adj.
Adj = ![\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26-3%5C%5C5%2611%5Cend%7Barray%7D%5Cright%5D%20%5E%7BT%7D)
= ![\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%265%5C%5C-3%2611%5Cend%7Barray%7D%5Cright%5D)
.
Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.
Therefore A' = (1/|A|)(Adj A),
or, A' = ![(1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right]](https://tex.z-dn.net/?f=%281%2F4%29%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%265%5C%5C-3%2611%5Cend%7Barray%7D%5Cright%5D)
,
or, A' = .
Therefore, the inverse of the matrix is the matrix .
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Answer:
k = 27/5
Step-by-step explanation:
Divide 5 on bot sides
5k/5 = 27/5
k= 27/5
so, k = 27/5 OR 5.4
Answer:
80 units
Step-by-step explanation:
When a figure is dilated by 2, its side measurements are halved. The figure you're seeing shows the quadrilateral <em>after </em>dilation (we can tell by the apostrophes); if U'R' is 40, UR will have to be 80.
As you said it was dropped so in that case I'll take 78.4 meters as the height..
we know that
h = ut + 0.5*g*t(sqr)
t(sqr) = 78.4/(0.5*9.8) [g = 9.8 ms-2]
t = √16
t = 4
So it'd take 4 seconds
Answer:
$3
Step-by-step explanation:
