CUET PG 2021 — Mathematics PYQ
CUET PG | Mathematics | 2021If A=(abamp;bamp;a) and A2=(αβamp;βamp;α)
Choose the correct answer:
- A.
α=2ab, β=2ab
- B.
α=a2+b2, β=2ab
α=a2+b2, β=2ab
Explanation
1. Matrix Multiplication
Given:
We calculate A2 as A×A:
2. Performing the Multiplication
To multiply the matrices, we multiply the rows of the first matrix by the columns of the second:
-
Top-left element: (a×a)+(b×b)=a2+b2
-
Top-right element: (a×b)+(b×a)=ab+ba=2ab
-
Bottom-left element: (b×a)+(a×b)=ba+ab=2ab
-
Bottom-right element: (b×b)+(a×a)=b2+a2
So, the result is:
3. Comparing with the Given Matrix
We are given:
By comparing the corresponding elements of the two matrices, we get:
Final Result:
The values of α and β are:
-
α=a2+b2
-
β=2ab
Explanation
1. Matrix Multiplication
Given:
We calculate A2 as A×A:
2. Performing the Multiplication
To multiply the matrices, we multiply the rows of the first matrix by the columns of the second:
-
Top-left element: (a×a)+(b×b)=a2+b2
-
Top-right element: (a×b)+(b×a)=ab+ba=2ab
-
Bottom-left element: (b×a)+(a×b)=ba+ab=2ab
-
Bottom-right element: (b×b)+(a×a)=b2+a2
So, the result is:
3. Comparing with the Given Matrix
We are given:
By comparing the corresponding elements of the two matrices, we get:
Final Result:
The values of α and β are:
-
α=a2+b2
-
β=2ab

