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Question

Consider the following statements:
1. The matrix
121a2a1b2b1 is singular.
2. The matrix
c2c1a2a1b2b1 is non-singular.
Which of the above statements is/are correct?

A
1 only
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B
2 only
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C
Both 1 and 2
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D
Neither 1 nor 2
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Solution

The correct option is A 1 only
For matrix
∣ ∣121a2a1b2b1∣ ∣

C2C22C1

∣ ∣101a01b01∣ ∣ The determinant is 0. So the matrix is singular.

For matrix,
∣ ∣c2c1a2a1b2b1∣ ∣

C2C22C1

∣ ∣c01a01b01∣ ∣ The determinant is 0. So the matrix is singular.
Thus, only 1 is true.
Hence, option A is correct.

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