Find a basis of the subspace of R* defined by the equation 5x1 - 7x2+8x3 6х4 = 0. 9. 9. 9. Basis: 9. 2. 2.
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- Diagonalize B [61] (by finding P and D) or explain why B isn't diagonalizable.Determine whether 2 × 2 matrix form a subspace where determinant of matrix is zero.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 – x²Explain why v = ( 1, 0, -1) cannot be a row of A and also in the nullspace.State the dimension of the following subspace, The solution space {(a,b,c): a-3b+c=0, b-2c=0, 2b-c=0} Answer: