If A'=\(\begin{bmatrix}-2&3\\1&2\end{bmatrix}\)and B=\(\begin{bmatrix}-1&0\\1&2\end{bmatrix}\),then find (A+2B)'
If A'=\(\begin{bmatrix}-2&3\\1&2\end{bmatrix}\)and B=\(\begin{bmatrix}-1&0\\1&2\end{bmatrix}\),then find (A+2B)'
Solution and Explanation
We know that A=(A')'
so A=\(\begin{bmatrix}-2&1\\3&2\end{bmatrix}\)
so A+2B=\(\begin{bmatrix}-2&1\\3&2\end{bmatrix}\)+2\(\begin{bmatrix}-1&0\\1&2\end{bmatrix}\)
=\(\begin{bmatrix}-2&1\\3&2\end{bmatrix}\)+\(\begin{bmatrix}-2&0\\2&4\end{bmatrix}\)=\(\begin{bmatrix}-4&1\\5&6\end{bmatrix}\)
so (A+2B)'=\(\begin{bmatrix}-4&5\\1&6\end{bmatrix}\)
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Concepts Used:
Transpose of a Matrix
The matrix acquired by interchanging the rows and columns of the parent matrix is called the Transpose matrix. The transpose matrix is also defined as - “A Matrix which is formed by transposing all the rows of a given matrix into columns and vice-versa.”
The transpose matrix of A is represented by A’. It can be better understood by the given example:
Now, in Matrix A, the number of rows was 4 and the number of columns was 3 but, on taking the transpose of A we acquired A’ having 3 rows and 4 columns. Consequently, the vertical Matrix gets converted into Horizontal Matrix.
Hence, we can say if the matrix before transposing was a vertical matrix, it will be transposed to a horizontal matrix and vice-versa.
Read More: Transpose of a Matrix