Question

How do you simplify \[\left[ {\begin{array}{*{20}{c}}
  {1.35} \\
  {1.24} \\
  {6.10}
\end{array}\,{\text{ }}\begin{array}{*{20}{c}}
  {5.80} \\
  {14.32} \\
  {35.26}
\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}
  {0.45} \\
  {1.94} \\
  {4.31}
\end{array}\,{\text{ }}\begin{array}{*{20}{c}}
  {3.28} \\
  {16.72} \\
  {21.30}
\end{array}} \right]?\]

Answer 1

Hint: In mathematics, Matrix can be defined as the set of numbers which are arranged in the rows and the columns so as to form the rectangular array. The numbers arranged in the matrix are known as the elements or the entries of the matrix. Here, the order of both the matrices are the same, and hence addition of the matrix is possible and so add the respective elements of the matrix of the first matrix with the second matrix and simplify for the resultant required values.

Complete step by step solution:
Take the given expressions –
\[\left[ {\begin{array}{*{20}{c}}
  {1.35} \\
  {1.24} \\
  {6.10}
\end{array}\,{\text{ }}\begin{array}{*{20}{c}}
  {5.80} \\
  {14.32} \\
  {35.26}
\end{array}} \right] + \left[ {\begin{array}{*{20}{c}}
  {0.45} \\
  {1.94} \\
  {4.31}
\end{array}\,{\text{ }}\begin{array}{*{20}{c}}
  {3.28} \\
  {16.72} \\
  {21.30}
\end{array}} \right]\]
Add the corresponding element of first matrix with the elements of the second matrix –
\[ = \left[ {\begin{array}{*{20}{c}}
  {1.35 + 0.45} \\
  {1.24 + 1.94} \\
  {6.10 + 4.31}
\end{array}\,{\text{ }}\begin{array}{*{20}{c}}
  {5.80 + 3.28} \\
  {14.32 + 16.72} \\
  {35.26 + 21.30}
\end{array}} \right]\]
Simplify the above expression finding the sum of the terms –
\[ = \left[ {\begin{array}{*{20}{c}}
  {1.8} \\
  {3.18} \\
  {10.41}
\end{array}\;{\text{ }}\begin{array}{*{20}{c}}
  {9.08} \\
  {31.04} \\
  {56.56}
\end{array}} \right]\]
This is the required solution.

Note: Don’t be confused between the two terms determinants and the matrices. Determinant is defined as the square matrix with the same number of rows and columns whereas the matrix is expressed as the rectangular grid of numbers and number of rows and the columns may not be the same. The plural of the Matrix is known as the Matrices. Remember for addition of matrices, the number of rows and number of columns in both of the matrices should be the same.