To solve x+Y = 3; 3r- 2y -4 = 0 bY determinant method find D
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1 -1 1], [0 -2 1], [1 0 3]} Compute a determinant to show that S is a basis for R^3. Justify. Use the Gram-Schmidt method to find an orthonormal basis. Let A and B n times n matrices. If A^2 = A, what are the possible values of det(A)? If AB is invertible, is BA invertible? If all cofactors of A are zero, is A invertible? If det(A) = 0, what is the possible rank of A? A = [x x x x x a b x d c x d e f x g h i] det A is a polynomial in x. Without computing det A, what is the degree of the polynomial? Justify using permutations, and then using cofactors. If the bottom 3 times 3 matrix is the identity matrix, which values of x give det A = 0? Let P be the plane in R^3 given by 3x + 2y - z = 0. Find a basis for the subspace P in R^3. Find a basis for the orthogonal complement P Justify using a nullspace computation. Find a basis for the orthogonal complement P Justify using the cross product. S = {[2 3 1], [1 -1 0], [7 3 2]} Show that the vectors in S are coplanar. If A is a matrix with these columns, give the dimensions of the four fundamental subspaces of A. Solve the following linear system using Cramer's Rule: {2x + y + z = 3 x - y - z = 0 x + 2y + z = 0
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