Find a basis of the subspace of R4 defined by the equation -8x17x2 + 4x3 + 5x4 = 0. Basis: 9.
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![Find a basis for the space of 2 × 2 lower triangular matrices.
Basis
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- define (2a - b + 4c, 3a-c, 4b + c) as a linear combination of three nonzero vectorsDraw the result of -u+2u-w as a single vector.Consider below presented polynomials v1, v2, v3, v4in P2. v1 = 2t2 + t + 2 v2 =t2 - 2t v3 =5t2 – 5t + 2 v4 =-t2 - 3t – 2 Determine whether the vector v = t2 + t + 2 belong to span {v1, v2, v3, v4}or not.
- In each part, determine whether the vectors are linearly independent or are linearly dependent in P2. (a) 5 – x + 4x²,4 + 9x + 5x²,4 + 6x – 4x² (b) 1+4x + 4x,x + 5x,5 + 2x + 5x², 6 + 5x – x²Find a basis of the subspace of R' defined by the equation -5x1- 5x2+ 2x3 = 0. Basis:Find a basis of the subspace of IR defined by the equation 871 - 7x2 - 4z3 = 0. Basis: