What is the rank of the 3 x 4 matrix 1 1 2 0 A = 0 -2 2 0 0 1 -1 -1 1 (a) regarded as a matrix over R? (b) regarded as a matrix over F3? (c) regarded as a matrix over F2? Select one: O The ranks 3 in all cases The ranks are (a) 3 O The ranks are (a) 3 O (b) 3 (c) 2 (b) 2 (c) 1 The ranks are (a) 2 (b) 2 (c) 0 Rank 0 in all cases as the matrix is not invertible

Q: Find the matrix of the quadratic form 2x,² + 3x2² – x3² – 4x1x2 +2 x1X3 + 6x2X3

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Q: Diagonalize the matrices below, if possible: (a) [1 0 3 2 1 2 0 0 2] (b) [3 1 1 −4 −2 −5 2 2 5]

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