1. Find the basis and dimension of the following system of linear equations: x1 + 2x2 – 2x3 – x4 = 0 2x1 + 5x2 – 3x3 – X4 = 1 Зх, + 8х, —4x3 — Х4 3D 2 X1 + 5x2 + x3 + 2x4 = 3 2. Verify Calay-Hamilton theorem for the following matrix: (2 1 -1 A = 3 1 \1 0 2 3. Find the Eigen value of the following matrix: 3 1 B = 2 4 2 1 1 123

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