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Anastaziya [24]
3 years ago
12

Find the inverse of ????−7 −2

Mathematics
1 answer:
Masja [62]3 years ago
6 0

Answer:

A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

Step-by-step explanation:

A=\begin{bmatrix}-7 & -2\\ 4 & 1\end{bmatrix}

det\ A=-7\times 1-(-2)\times 4\\\Rightarrow det\ A=1

A^{-1}=\frac{1}{det\ A}\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A^{-1}=\frac{1}{1}\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

\therefore A^{-1}=\begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}

A.A^{-1}=\begin{bmatrix}-7 & -2\\ 4 & 1\end{bmatrix}\times \begin{bmatrix}1 & 2\\ -4 & -7\end{bmatrix}\\\Rightarrow A.A^{-1}=\begin{pmatrix}\left(-7\right)\cdot \:1+\left(-2\right)\left(-4\right)&\left(-7\right)\cdot \:2+\left(-2\right)\left(-7\right)\\ 4\cdot \:1+1\cdot \left(-4\right)&4\cdot \:2+1\cdot \left(-7\right)\end{pmatrix}\\\Rightarrow A.A^{-1}=\begin{pmatrix}1&0\\ 0&1\end{pmatrix}

Hence, confirmed

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Answer:

<em>The probability that the next flower seed will sprout is 0.667 or 66.7%</em>

Step-by-step explanation:

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The experimental or empirical probability can be defined as the ratio of the number of times an event occurs to the total number of times the random activity was performed.

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\displaystyle P(A)=\frac{32}{48}=\frac{2}{3}=0.667

Thus, the probability that the next flower seed will sprout is 0.667 or 66.7%

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Step-by-step explanation:

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