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UPSC NDA Math Model Paper 1

Question : 20 of 120

Marks: +1, -0

\begin{vmatrix} x & y & z \\ a & b & c \\ x+a & y+b & z+c \end{vmatrix}

Solution:

\begin{vmatrix} x & y & z \\ a & b & c \\ x+a & y+b & z+c \end{vmatrix}

Apply

R_1 \rightarrow R_1+R_2

\begin{vmatrix} x+a & y+b & z+c \\ a & b & c \\ x+a & y+b & z+c \end{vmatrix}

As we can see that the first and the third row of the given matrix are equal.

We know that, if any two rows (columns) of a matrix are same then the value of the determinant is zero.

\begin{vmatrix} x & y & z \\ a & b & c \\ x+a & y+b & z+c \end{vmatrix}=0

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