the first mention of the world bang is found in
Answers
Explanation:
Step-by-step explanation:
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−4
−4
5
5
−2
−5
1
1
1
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\begin{gathered}\boxed{\tt{ \: OP \: R_2 \: \to \: R_2 \: - \: R_1 \: \: \: \: [in \: both \: determinants]}} \\ \end{gathered}
OPR
2
→R
2
−R
1
[inbothdeterminants]
\begin{gathered}\rm \: = \: \dfrac{1}{2} \left | \begin{array}{ccc} - 4 &5&1 \\ 4&2&0 \\ 5& - 5&1\end{array}\right| + \dfrac{1}{2} \left | \begin{array}{ccc} - 4 &5&1 \\0& - 7&0 \\ 5& - 5&1\end{array}\right| \\ \end{gathered}
=
2
1
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−4
4
5
5
2
−5
1
0
1
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+
2
1
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−4
0
5
5
−7
−5
1
0
1
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\begin{gathered}\boxed{\tt{ \: OP \: R_3 \: \to \: R_3 \: - \: R_1 \: \: \: \: [in \: both \: determinants]}} \\ \end{gathered}
OPR
3
→R
3
−R
1
[inbothdeterminants]
\begin{gathered}\rm \: = \: \dfrac{1}{2} \left | \begin{array}{ccc} - 4 &5&1 \\ 4&2&0 \\ 9& - 10&0\end{array}\right| + \dfrac{1}{2} \left | \begin{array}{ccc} - 4 &5&1 \\0& - 7&0 \\ 9& - 10&0\end{array}\right| \\ \end{gathered}
=
2
1
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−4
4
9
5
2
−10
1
0
0
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+
2
1
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−4
0
9
5
−7
−10
1
0
0
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Now, Expanding along 3rd column, we get
\begin{gathered}\rm \: = \: \dfrac{1}{2} ( - 40 - 18)+ \dfrac{1}{2} (0 + 63) \\ \end{gathered}
=
2
1
(−40−18)+
2
1
(0+63)
\begin{gathered}\rm \: = \: \dfrac{1}{2} ( - 58)+ \dfrac{1}{2} (63) \\ \end{gathered}
=
2
1
(−58)+
2
1
(63)
\begin{gathered}\rm \: = \: \dfrac{ - 58}{2} + \dfrac{63}{2} \\ \end{gathered}
=
2
−58
+
2
63
\begin{gathered}\rm \: = \: \dfrac{ - 58 + 63}{2}\\ \end{gathered}
=
2
−58+63
\begin{gathered}\rm \: = \: \dfrac{5}{2}\\ \end{gathered}
=
2
5
Hence,
\begin{gathered}\boxed{\tt{ \rm \:\dfrac{1}{2} \left | \begin{array}{ccc} - 4 &5&1 \\ 0&7&1 \\ 5& - 5&1\end{array}\right| + \dfrac{1}{2} \left | \begin{array}{ccc} - 4 &5&1 \\ - 4& - 2&1 \\ 5& - 5&1\end{array}\right| = \: \dfrac{5}{2}}}\\ \end{gathered}
2
1
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−4
0
5
5
7
−5
1
1
1
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+
2
1
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−4
−4
5
5
−2
−5
1
1
1
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=
2
5
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ADDITIONAL INFORMATION
1. The determinant value remains unaltered if rows and columns are interchanged.
2. The determinant value is 0, if two rows or columns are identical.
3. The determinant value is multiplied by - 1, if successive rows or columns are interchanged.
4. The determinant value remains unaltered if rows or columns are added or subtracted.
Answer:
The universal origin story known as the Big Bang postulates that, 13.7 billion years ago, our universe emerged from a singularity — a point of infinite density and gravity — and that before this event, space and time did not exist (which means the Big Bang took place at no place and no time)