Evaluate | * 20 r 1&x&y 1& x + y &y 1&x& x + y |

Let = | * 20 r 1&x&y 1& x + y &y 1&x& x + y | Applying R 2 - R 1 and R 3 - R 1 , we get | * 20 r 1&x&y 0&y&0 0&0&x | Expanding along C 1 , we get 1 y x = xy. Using properties of determinants in questions 11 to15, prove that:

Determinants — Class 12 Maths Solution

ncert misc SA NCERT,Misc.Q.10,Page.142

Question

Evaluate $\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&x&y\\1&{x + y}&y\\1&x&{x + y}\end{array}} \right|$

Step-by-step Solution

Let $\Delta$ $=$ $\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&x&y\\1&{x + y}&y\\1&x&{x + y}\end{array}} \right|$

Applying ${R_2} \to {R_2} - {R_1}$ and ${R_3} \to {R_3} - {R_1},$

we get
$\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&x&y\\0&y&0\\0&0&x\end{array}} \right|$

Expanding along ${C_1}$,

we get
$1 \times y \times x = xy.$
Using properties of determinants in questions 11 to15, prove that:

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