LINEAR ALGEBRA (TRUE/FALSE) EXAM Q&A

LINEAR ALGEBRA (TRUE/FALSE) EXAM
Q&A
A linear system whose equations are all homogeneous must be consistent. - Answer-
True

Multiplying a linear equation through by zero is an acceptable elementary row op. -
Answer-False

x-y=3
2x-2y=k
The linear system cannot have a unique solution, regardless of the value of k. - Answer-
True

A single linear equation with two or more unknowns must always have infinitely many
solutions. - Answer-True

If the number of equations in a linear system exceeds the number of unknowns, then
the system must be inconsistent. - Answer-False

If each equation is consistent linear system is multiplied through by a constant c, then
all solutions to the new system can be obtained by multiplying solutions from the original
system by c. - Answer-False

Elementary row ops permit one equation in a linear system to be subtracted from
another. - Answer-True

If a matrix is in reduced row echelon form, then it is also in row echelon form. - Answer-
True

If an elementary row op is applied to a matrix that is in row echelon form, the resulting
matrix will still be in row echelon form. - Answer-False

Every matrix has a unique row echelon form. - Answer-False

A homogeneous linear system in n unknowns whose corresponding augmented matrix
has a reduced row echelon form with r leading 1's has n-r free variables. - Answer-True

All leading 1's in a matrix in row echelon form must occur in different columns. - Answer-
True

If every column of a matrix in row echelon form has a leading 1 then all entries that are
not leading 1's are zero. - Answer-False

, If a homogeneous linear system of n equations in n unknowns has a corresponding
augmented matrix with a reduced row echelon form containing n leading 1's, then the
linear system has only the trivial solution. - Answer-True

If the reduced row echelon form of the augmented matrix for a linear system has a row
of zeros, then the system must have infinitely many solutions. - Answer-False

If a linear system has more unknowns than equations, then it must have infinitely many
solutions. - Answer-False

If A and B are 2x2 matrices, then AB=BA. - Answer-False

The ith row vector of a matrix product AB can be computed by multiplying A by the ith
row vector of B. - Answer-False

tr(AB) = tr(A)tr(B) - Answer-False

(AB)transpose=(A)trans(b)trans - Answer-False

tr(A trans)=tr(A) - Answer-True

tr(cA)=ctr(A) - Answer-True

AC=BC, then A=B - Answer-False

If B has a column of zeros, then so does AB if this product is defined. - Answer-True

If B has a column of vectors, then so down BA if this product is defined. - Answer-False

A product of any number of invertible matrices is invertible, and the inverse of the
product is the product of the inverses in the reverse order. - Answer-True

(AB)trans=(B)trans(A)trans - Answer-True

The transpose of a product of any number of matrices is the product of the transposes
in the reverse order - Answer-True

two nxn matrices are inverses of one another iff AB=BA=0 - Answer-False

A^2-B^2=(A-B)(A+B) - Answer-False

(AB)^-1=A^-1B^-1 - Answer-False

(kA+B)trans=k(A)trans + (B)trans - Answer-True

If A is an invertible matrix, then so is A trans - Answer-True