The result of the product of the two matrices is: [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] =\left[\begin{array}{cc}1&0\\ 0&1\end{array}\right] [/tex]
How to calculate the product of matrices
The product equation is given as:
[tex]\left[\begin{array}{cc}2&7\\1&3\end{array}\right] \left[\begin{array}{cc}-3&7\\1&-2\end{array}\right] = \left[\begin{array}{cc}a&b\\c&d\end{array}\right] [/tex]
Multiply the rows of the first matrix, by the columns of the second matrix.
So, we have:
[tex]\left[\begin{array}{cc}2 \times -3 + 7 \times 1&2 \times 7 + 7 \times -2\\1 \times -3 + 3 \times 1&1 \times 7 + 3 \times -2\end{array}\right] = \left[\begin{array}{cc}a&b\\c&d\end{array}\right] [/tex]
Evaluate the products
[tex]\left[\begin{array}{cc}-6 + 7&14 -14\\ -3 + 3&7 -6\end{array}\right] = \left[\begin{array}{cc}a&b\\c&d\end{array}\right] [/tex]
Evaluate the sum and the differences
[tex]\left[\begin{array}{cc}1&0\\ 0&1\end{array}\right] = \left[\begin{array}{cc}a&b\\c&d\end{array}\right] [/tex]
Rewrite the above equation as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] =\left[\begin{array}{cc}1&0\\ 0&1\end{array}\right] [/tex]
Hence, the result of the product of the two matrices is:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] =\left[\begin{array}{cc}1&0\\ 0&1\end{array}\right] [/tex]
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