Question:
If the matrix Mr is given by Mr=\(\begin{pmatrix}r &r-1 \\ r-1&r \end{pmatrix}\) for r=1,2,3....then det(M1)+det(M2)+.......+det(M2008)=
If the matrix Mr is given by Mr=\(\begin{pmatrix}r &r-1 \\ r-1&r \end{pmatrix}\) for r=1,2,3....then det(M1)+det(M2)+.......+det(M2008)=
Updated On: Jul 28, 2023
- 2007
- 2008
- (2008)2
- (2007)2
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The Correct Option is C
Solution and Explanation
The correct answer is option (C): (2008)2
\(det(M_r)=\begin{vmatrix} r &r-1 \\ r-1&r \end{vmatrix}=2r-1\)
\(\sum_{r=1}^{2008} det(M_r)=2\sum_{r=1}^{2008}(r-2008)\)
\(=2\times\frac{2008\times2009}{2}-2008\)
\(=(2008)^2\)
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Concepts Used:
Matrix Transformation
The numbers or functions that are kept in a matrix are termed the elements or the entries of the matrix.
Transpose Matrix:
The matrix acquired by interchanging the rows and columns of the parent matrix is termed the Transpose matrix. The definition of a transpose matrix goes as follows - “A Matrix which is devised by turning all the rows of a given matrix into columns and vice-versa.”