![]() ![]() ![]() The set of upper triangular n×n matrices is a subspace Two subsets of a vector space V that span the sameĬ. Every subset of a vector space V that contains the zeroī. The union of any two subspaces of a vector space V is The intersection of any two subspaces of a vector spaceĭ. Every vector space is a subspace of itself.Ĭ. Every subspace of a vector space is itself a vector space.ī. Which of the following vectors are inspan? įind the value ofm such that the vector (m, 7 ,−4) is a Which of the following are linear combinations ofĪ=, B=, C= ? A. The system of equations (λI + A)x = 0 has nontrivial The system of equations (λI - A)x = 0 has only trivialĬ. The system of equations (λI + A)x = 0 has only trivialī. If W is a subspace of a finite-dimensional vector space V, IfTA:Rn→Rnand ifTA(x) = 0 for every vectorxinRn,ĭoes the vectorsv 1 = (− 3 ,7) andv 2 = (5,5) form a basisĪre the vectorsv 1 = (2, 0 ,−1), v 2 = (4, 0 ,7), andv 3 = If A is an m×n matrix, then the codomain of the trans. The linear system Ax = 4x hasĪ unique solution if and only if. If A is an n×n matrix that is not invertible, then the linear Responding augmented matrix has a reduced row echelonĪ linear system is called consistent if it has Ax = b has more than one solution for every n× 1Ī homogeneous linear system in n unknowns whose cor. Ax = b is inconsistent for every n×1 matrix b.ĭ. A cannot be expressed as a product of elementary ma-Ĭ. Of the following statement is equivalent:ī. Let A be an n×n matrix, and A is invertible. Tity matrix by performing a single elementary row opera. IfAandBare invertible matrices with the same size, thenĪ matrix E is called.if it can be obtained from an iden. LINEAR ALGEBRA (MTS4 B04) CORE COURSE - BSc MATHEMATICS IfAandBare symmetric matrices of same order, thenįor all sqaure matricesAandB, is it true thatdet(A+B) =Ī matrix that is both symmetric and upper triangular must If A and B are square matrices of the same order, then ![]()
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