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2. (a) Determine if B = 1 0 1 1 , 1 0 −2 1 ,...

2. (a) Determine if B = 1 0 1 1 , 1 0 −2 1 , −2 0 7 −2 spans L2×2. (Here L2×2 denote vector space of all 2 × 2 lower triangular real matrices.)

(b) Check if S2 = x 2 + x + 1, 2x − 1, 3x 2 − 5 spans P2(x) (Here P2(x) is a vector space containing polynomials of degree less than or equal to 2.)

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