Linear Algebra Key PASSED Exam Questions and CORRECT Answers
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Course
Linear Algebra
Institution
Linear Algebra
Null Space Solution Space of a homogenous system
Nullity Dimension of the Null space
Dimension Number of vectors that form a basis. (non zero rows in a rref matrix
Linearly dependent When the sum of subspace multiplied by a non-zero constant
equals the zero vector
Gram Schmidt
Consistent ha...
Linear Algebra Key PASSED Exam Questions and CORRECT Answers Null Space ✔✔✔ Solution Space of a homogenous system Nullity ✔✔✔ Dimension of the Null space Dimension ✔✔✔ Number of vectors that form a basis. (non zero rows in a rref matrix Linearly dependent ✔✔✔ When the sum of subspace multiplied by a non -zero constant equals the zero vector Gram Schmidt ✔✔✔ Consistent ✔✔✔ has a solution Projection ✔✔✔ [(V ,W 1)/(W 1,W1)]W1+[(V ,W 2)/(W 2,W2)]W2...... Homogenous System ✔✔✔ Ax=0 and the application of this (this process is how we find eigen vectors Span ✔✔✔ Any linear combination of a set of vectors that can combine to form any real vector in R^n Basis ✔✔✔ A linearly independent set of vectors that span V . (smallest set of vectors in the span that can linearly combine to form any vector in V) Trivial ✔✔✔ a solution in which every unknown equals zero. always a solution to a homogenous system Inconsistent ✔✔✔ Has no solution Non-Trivial ✔✔✔ Solution to a homogenous system in which not all unknowns are zero Diagonal Matrix ✔✔✔ Upper Triangular Matrix ✔✔✔ Lower Triangular Matrix ✔✔✔ Symmetric Matrix ✔✔✔ if A^T=A Skew Symmetric Matrix ✔✔✔ If A^T= -A Matrix Multiplication ✔✔✔ If A is an MxN matrix and B is an M'xN' matrix.(Rows)*(Columns A)=C . inner matrix dimensions must agree (N = M'). Resulting matrix will have dimension of outer matrix dimensions. C is a MxN' matrix Non-singular Matrix ✔✔✔ a square matrix that has an inverse. Has a non zero determinant. A is an nxn matrix and Det(A)~=0 (Invertible) Singular Matrix ✔✔✔ a square matrix that has no inverse. A is an nxn matrix and Det(A)=0 (Non -invertible) Det(A^T)= ✔✔✔ Det(A) If B results from Switchi ng one row(column) of A with another row of A then ✔✔✔ Det(B)= -
Det(A) If two rows(Columns) of A are equal then ✔✔✔ Det(A)= 0
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