b Set C x yx y E R Vector Addition x1 y1 x2 y2 x1 x2 1 y

(b) Set C = {(x, y)x, y E R}. Vector Addition: (x1 y1) + (x2 y2) = (x1 + x2 +1, y1 + y2 + 1) Scalar Multiplication: The two vectors (x1 y2), (x2 y2) are equal if and only if x1 = x2, y1 = y2. Is the set R = {(2, 1) (9,7)} linearly independent in the vector space C

Solution

For a set to be linearly independent, their determinant should not be equal to zero , otherwise its elements are linearly dependent.

Here for set R= {(2,1)(9,7) } , we have

R= | 2 1 |

| 9 7 | = 2 x 7 - 1 x 9

= 14 - 9 = 5

that is not equal to zero that means it is true that set R{(2,1),(9,7) } is linearly independent.