Exam (elaborations)
MATRICES TRUE/FALSE QUESTIONS AND ANSWERS
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MATRICES TRUE/FALSE QUESTIONS AND ANSWERS
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MATRICES TRUE/FALSE QUESTIONS AND ANSWERSA linear system can have exactly two solutions. - Answers -False
Two systems of linear equations are equivalent when they have the same solution set. -
Answers -True
A system of three linear equations in two variables is always inconsistent. - Answers -
False
A 6x3 matrix has six rows. - Answers -True
Every matrix is row-equivalent to a matrix in row-echelon form. - Answers -True
If the row-echelon form of the augmented matrix of a system of linear equations
contains the row [1 0 0 0 0] , then the original system is inconsistent. - Answers -False
The inverse of the inverse of a nonsingular matrix A, (A^-1)^-1, is equal to A itself. -
Answers -True
The matrix [a b]
[c d]
is invertible when ab - dc != 0. - Answers -False
If A is a square matrix, then system of linear equations Ax = b has a unique solution. -
Answers -False
To find the determinant of a triangular matrix, add the entries on the main diagonal. -
Answers -False
To find the determinant of a matrix, expand by cofactors in any row or column. -
Answers -True
When expanding by cofactors, you need not evaluate the cofactors of zero entries. -
Answers -True
Interchanging two rows of a square matrix changes the sign of its determinant. -
Answers -True
Multiplying a column of a square matrix by a nonzero constant results in the determinant
being multiplied by the same nonzero constant. - Answers -True
If two rows of a square matrix are equal, then its determinant is 0. - Answers -True
Adding a multiple of one column of a square matrix to another column changes only the
sign of the determinant. - Answers -False
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