Question

**True or False?** *(Make sure to justify your
answer.)*

For this question let ?A be a non-zero ?×?m×n matrix, and ?B an invertible ?×?n×n matrix.

If {?1,...,??}{x1,...,xk} is a basis for null(?)null(A), then dim(null(??))=?dim(null(AB))=k.

Answer #1

Indicate whether each statement is True or False.
Briefly justify your answers. Please answer all of questions
briefly
(a) In a vector space, if c⊙⃗u =⃗0, then c= 0.
(b) Suppose that A and B are square matrices and that AB is a
non-zero diagonal matrix. Then A is non-singular.
(c) The set of all 3 × 3 matrices A with zero trace (T r(A) = 0)
is a vector space under the usual matrix operations of addition and
scalar...

True or false; for each of the statements below, state whether
they are true or false. If false, give an explanation or example
that illustrates why it's false.
(a) The matrix A = [1 0] is not invertible.
[1 -2]
(b) Let B be a matrix. The rowspaces row (B), row (REF(B)) and
row (RREF(B)) are all equivalent.
(c) Let C be a 5 x 7 matrix with nullity 3. The rank of C is
2.
(d) Let D...

Answer all of the questions true or false:
1.
a) If one row in an echelon form for an augmented matrix is [0 0 5
0 0]
b) A vector b is a linear combination of the columns of a matrix A
if and only if the
equation Ax=b has at least one solution.
c) The solution set of b is the set of all vectors of the form u =
+ p + vh
where vh is any solution...

True or False
(5). Suppose the matrix A and B are both invertible, then (A +
B)−1 = A−1 + B−1
. (6). The linear system ATAx = ATb is always consistent for any
A ∈ Rm×n, b ∈Rm .
(7). For any matrix A ∈Rm×n , it satisﬁes dim(Nul(A)) =
n−rank(A).
(8). The two linear systems Ax = 0 and ATAx = 0 have the same
solution set.
(9). Suppose Q ∈Rn×n is an orthogonal matrix, then the row...

True or False? No reasons needed.
(e) Suppose β and γ are bases of F n and F m, respectively.
Every m × n matrix A is equal to [T] γ β for some linear
transformation T: F n → F m.
(f) Recall that P(R) is the vector space of all polynomials with
coefficients in R. If a linear transformation T: P(R) → P(R) is
one-to-one, then T is also onto.
(g) The vector spaces R 5 and P4(R)...

True or False? Justify your answer. If the kernel of matrix A
contains two different vectors, then homogeneous system A.x=θ has
infinitely many solutions.

True or false justify your answer
1-The higher the price of X1 the flatter the B.L would be
2-Consumer equilibrium requires that indifference curve intersects
the B.L
3-If B.L slope =zero, then a consumer can have an extra unit of
good X without paying additional money
4-Cash subsidy is preferred to gift certificate from the store
owner view point

This is a TRUE-FALSE Question with justification.
If Q is an orthogonal n×n matrix, then Row(Q) =
Col(Q).
The Answer to this is TRUE. I want to know a solid
reasoning/explanation for it.
In one of the answers, it says that " Since Q is orthogonal,
QTQ = I, so Q is invertible, hence Row(Q) = Col(Q) =
Rn. But my question is: Why is it that for an invertible
matrix, Row(Q) = Col (Q) ?
Any other explanation that...

True False questions. Make sure you EXPLAIN EACH ANSWER.
2.19) Suppose that W is a four-dimensional subspace of R7 that
is spanned by {X1,X2,X3,X4}. Then one of the Xi must be a linear
combination of the others.
2.20)Suppose that A is a 3 x 5 matrix such that the vectors X =
[1,1,1,1,1]^t, Y= [0,1,1,1,1]^t, and Z = [0,0,1,1,1]^t belong to
the nullspace of A.
2.20a) The rows of A are dependent.
2.20b) AX= B has a solution for all...

True or false. If your answer is false, you must justify
your answer with a one sentence explanation to receive any
credit.
An asset depreciated in the 3-years MACRS class will have book
value of 0 at the end of 3 years.
The discounted payback period will always be no shorter than
the undiscounted payback period.
If the internal rate of return on an investment is positive,
then the investment’s net present value must be positive.
You are purchasing a...

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