math 123 true false (2)

. The system of equations ax + by = 0; cx + dy = 0 has at least one solution regardless of the values of a, b, c, d.

T

If a system of linear equations is inconsistent, then it has infinitely many solutions.  

F

If a system of linear equations has infinitely many solutions, then it may be inconsistent.

F

Some row reduced matrices have a 2 in the top left-hand corner.  

F

If two of the equations in a system of linear equations are inconsistent, then the whole system is inconsistent.

T

If the row reduced form of the augmented matrix corresponding to a system of linear equations has a row of zeros, then there are infinitely many solutions.

F

The system x + y + z = 1; x = y; y = z, y = 1 is inconsistent.

T

If the row reduced form of a matrix has more than one non-zero entry in any row, then the corresponding system of linear equations has infinitely many solutions.

F

If the graphs of two linear equations are not parallel, then there is a unique solution to the system.  

T

If quantity x is twice quantity y, then x − 2y = 0

T

When we row reduce a matrix, we must always turn each pivot into a 1 before clearing its column, or else errors will result.

F

The system x + y + z = 3; x = y; y = z, y = 1 is inconsistent.

F

Every system of three linear equations in three unknowns has at least one solution.  

F

A row reduced matrix always has a 1 in the second column of the second row.

F

A system of linear equations either has no solutions, one solution, or infinitely many solutions

T

In the row-reduced form of a matrix, the first nonzero entry in each row is a 1.

T

If two linear equations have the same graph, then the asociated system has infinitely many solutions.

T

If quantity x is twice quantity y, then 2x − y = 0

F

If the graphs of two linear equations are not parallel, then there may be no solution to the system.

F

A system of three equations in two unknowns cannot have a solution.  

F

If AB ≠ 0, then neither A nor B is a zero matrix.

T

"Not invertible" is the same thing as "singular."

T

If A and B are diagonal 3 × 3 matrices, then AB = BA.

T

If a system of linear equations is represented by AX = B and A is invertible, then the system has a unique solution.

T

If defined, a column times a row is never a 1 × 1 matrix.

F

If AB = 0, then either A or B is a zero matrix.

F

If two rows of a square matrix are equal, then the matrix is singular.

T

If defined, a row times a column is always a 1 × 1 matrix.

T

	1	2
	1	1

  is invertible.

T

If the row-reduced form of a square matrix contains a row of zeros, then the matrix is singular.  

T

The ij entry of the product AB is obtained by multiplying the ith row of A by the jth column of B.

T

If defined, a column times a row is always a 1 × 1 matrix.

F

A 2 × 3 matrix has three columns and two rows.

T

If the row-reduced form of a matrix is the identity, then the matrix is invertible.

T

	1	2
	2	1

  is singular.  

F

If a system of linear equations is represented by AX = B and A is not invertible, then the system has no solution.

F

If a system of linear equations is represented by AX = B and A is invertible, then the system has infinitely many solutions.

F

The transpose of a 5 × 6 matrix has six columns and five rows.  

F

If the row-reduced form of a matrix is the identity, then the matrix is singular.  

F

	1	1
	3	3

  is invertible.

F