Mathematics: 1. what is the smallest whole number greater than √30 + √50 + √110? 2. for how many single-digit positive integers d are there an integer n for which the units digit of [tex]d^{n}[/tex] is 6? 3. a rectangular prism with whole number dimensions has faces with areas 54, 72, and 108 square inches. how many cubic inches are there in its volume? 60 points! partial answers accepted as well.

Step-by-step explanation:Inverse of a matrix is given by,By using this property, Therefore, inverse of the given matrix will be...

1. what is the smallest whole number greater than

kbracey

06.12.2021

$\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}$

Step-by-step explanation:

Inverse of a matrix is given by,

$\begin{bmatrix}a & b\\ c & d\end{bmatrix}=\frac{1}{ad-bc}\begin{bmatrix}d & -b\\ -c & a\end{bmatrix}$

By using this property,

$\begin{bmatrix}5 & 4\\ 3 & 2\end{bmatrix}^{-1}=\frac{1}{(5\times 2-4\times 3)}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}$

$=-\frac{1}{2}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}$

$=\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}$

Therefore, inverse of the given matrix will be $\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}$

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