COMPASSLearning

Talk to us Register Login

CBSE Class 12 · DeterminantsLong Answer

Using properties of determinants, prove that

x x + 2 y x + y x + y x x + 2 y x + 2 y x + y x = 9 y^{2} (x + y) .

Answer: Proved

Solution

Apply

C_{1} \to C_{1} + C_{2} + C_{3}

; each entry of column

1

becomes

3 (x + y)

. Take it common:

= 3 (x + y) 111 x + y x x + 2 y x + 2 y x + y x .

Apply

R_{1} \to R_{1} - R_{2}

,

R_{3} \to R_{3} - R_{2}

and expand along

C_{1}

:

= 3 (x + y) [- (- y^{2} - 2 y^{2})] = 3 (x + y) \cdot 3 y^{2} = 9 y^{2} (x + y) .

Proved.

CBSE Class 12 Board · Subjective

Practise more: all CBSE board PYQs on Determinants →

More board questions on Determinants

If $A$ is a square matrix of order $2$ and $∣ A ∣ = - 2$ , then the value of $∣5 A ∣$ is:
CBSE 2024View solution →
If $123 23 a 111$ is a non-singular matrix and $a \in A$ , then the set $A$ is:
CBSE 2023View solution →
If $∣ A ∣ = ∣ k A ∣$ , where $A$ is a square matrix of order $2$ , then sum of all possible values of $k$ is:
CBSE 2023View solution →
If $(a, b), (c, d)$ and $(e, f)$ are the vertices of $Δ A B C$ and $Δ$ denotes the area of $Δ A B C$ , then $a b 1 c d 1 e f 1^{2}$ is equal to:
CBSE 2023View solution →
If $A$ is a square matrix of order $3$ and $∣ A ∣ = 5$ , then the value of $∣2 A^{'} ∣$ is:
CBSE 2020View solution →
If $A$ is a square matrix satisfying $A^{'} A = I$ , write the value of $∣ A ∣$ .
CBSE 2019View solution →