Consider the system of linear equations

x + 2y + z = 5

2x + ay + 4z = 12

2x + 4y + 6z = b

The values of a and b such that there exists a non-trivial null space and the system admits infinite solutions are

A linear transformation maps a point (𝑥, 𝑦) in the plane to the point (𝑥̂, 𝑦̂) according to the rule

𝑥̂ = 3𝑦, 𝑦̂ = 2𝑥.

Then, the disc 𝑥² + 𝑦² ≤ 1 gets transformed to a region with an area equal to _________ . (Rounded off to two decimals)

Use π = 3.14.