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Math
Algebra
Linear Algebra
Math 340 Midterm T/F Review
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Terms in this set (20)
A linear system of three equations can have exactly three different solutions
False; Linear systems can have either unique solution, no solution or infinite # of solutions
If A and B are NxN matrices and AB=identity matrix
False; A = [1, 1; -1, -1] B = [-1, -1; 1, 1] AB = [0, 0, 0, 0]
If A is an nxn matrix, then A+A^T is symmetric
True
If A is an nxn matrix and x is nx1, then Ax is a linear combination of the columns of A
True
Homogeneous Linear System is represented with:
Ax=0
Homogeneous linear systems are always consistent
True; always at least one solution (x = (0,0,0,...,0)) because homogeneous system is of form Ax = 0
The sum of two nxn upper triangular matrices is upper triangular
True
The sum of two nxn symmetric matrices is symmetric
True; Cij = aij + bij = bji + aji = Cji
If a linear system has a nonsingular coefficient matrix, then the system has a unique situation.
True. Ax =b => x = A^-1b
The product of two nxn nonsingular matrices is nonsingular
True; ABB^-1A^-1 = I AA^-1 = AA^-1 = I
A[0,0; 0,1] defines a matrix transformation that projects the vector [x, y] onto the y-axis.
True
Every matrix in row echelon form is also in reduced row echelon form.
False. Use [1, -1; 0, 1] as an example.
If the augmented matrices of two linear systems are row equivalent, then the systems have exactly the same solutions.
True. Flipping two rows are row equivalent; will lead to same RREF
If a homogeneous linear system has more equations than unknowns, then it has a nontrivial solution.
False.
The reduced row echelon form of a nonsingular matrix is an identity matrix.
True
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