Question

True or False?(AND WHY)

If **A** = [*a*1*...a**n*] and
**B** = [*b*1*... bm*] are two matrices
such that Span(*a*1*, ...,a**n*) =
Span(*b*1*, ..., bm*), then **A** and
**B** are row equivalent.

Answer #1

**Please feel free to ask any query in the comment
box**

Let A = {a1, . . . , ak} and B = {b1,. . . , bm} be two sets of
numbers. Consider the problem of finding the difference set of A
and B(A–B), i.e., the set of all elements of A that are not
elements of B.
a)Design a n O(nlogn) algorithm for solving this problem.
b)Show that the worst-case complexity of your algorithm is O(n
logn)

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...

Are the matrices A and B Row equivalent? Why or Why not?
A=
1
1
1
2
3
-1
-1
4
1
B =
1
0
-1
1
1
1
0
1
3

Hi, I know that if two matrices A and B are similar matrices
then they must have the same eigenvalues with the same geometric
multiplicities. However, I was wondering if that statement was
equivalent. In order terms, if two matrices have the same
eigenvalues with the same geometric multiplicities, must they be
similar? If not, is it always false?

True or False (Please explain)
1. If E and F are elementary matrices then C = E*F is
nonsingular.
2. If A is a 3x3 matrix and
a1+2a2-a3=0 then A must be
singular.
3. If A is a 3x3 matrix and
3a1+a2+4a3=b is consistent.

Explain why the set of vectors given in matrix form do not span
R3 : a1 b1 2a1
-3b1
a2 b2 2a2 -3b2
a3 b3 2a3 -3b3

Hi,
I know that if two matrices A and B are similar matrices then
they must have the same eigenvalues with the same geometric and
algebraic multiplicities. However, I was wondering if that
statement was equivalent. In order terms, if two matrices have the
same eigenvalues with the same algebraic multiplicities, must they
be similar? What about geometric multiplicities?

Given that A and B are n × n matrices and T is a linear
transformation. Determine which of the following is FALSE.
(a) If AB is not invertible, then either A or B is not
invertible.
(b) If Au = Av and u and v are 2 distinct vectors, then A is not
invertible.
(c) If A or B is not invertible, then AB is not invertible.
(d) If T is invertible and T(u) = T(v), then u =...

A four-input (A1, A2, B1, B2) and two-output (Y1, Y2) “BUT” gate
has the following behavior:
• Y1 is 1 if A1 and B1 are 1 but either A2 or B2 is 0
• Y2 is defined symmetrically
a. Write logic expressions for Y1 and Y2 outputs of the BUT
gate
b. Draw the corresponding logic diagram using AND gates, OR
gates, and inverters
c. Write a behavioral-style Verilog model for the BUT gate

Deside whether the statements below are true or false. If
true, explain why true. If false, give a counterexample.
(a) If a square matrix A has a row of zeros, then A is not
invertible.
(b) If a square matrix A has all 1s down the main diagonal,
then A is invertible.
(c) If A is invertible, then A−1 is invertible.
(d) If AT is invertible, then A is invertible.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 22 minutes ago

asked 34 minutes ago

asked 34 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago