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1
answer
Let \(A\) be a square matrix and \(p(\lambda)\) any polynomial. If \(\lambda\) is an eigenvalue of \(A\), show that \(p(\lambda)\) is an eigenvalue of the matrix \(p(A)\) with the same eigenvector.
answered
Jan 31
in
Mathematics
|
303
views
eigenvalue
matrix
eigenvector
vector
self-adjoint
solution
rank
1
answer
Let \(A \in M(n, \mathbb{F})\) have an eigenvalue \(\lambda\) with corresponding eigenvector \(v\). True or False
answered
Jan 31
in
Mathematics
|
246
views
eigenvalue
eigenvector
matrix
vector
self-adjoint
vectors
square
1
answer
Let \(M\) be a \(2 \times 2\) matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant \(c\). Which (if any) any of the vectors
answered
Jan 31
in
Mathematics
|
176
views
matrix
eigenvalue
eigenvector
vector
solution
self-adjoint
rank
1
answer
Let \(A\) and \(B\) be \(n \times n\) matrices with the property that \(A B=0 .\) For each of the following give a proof or counterexample.
answered
Jan 31
in
Mathematics
|
218
views
eigenvalue
eigenvector
invertible
matrix
proof
1
answer
Let \(A\) and \(B\) be \(n \times n\) matrices with \(A B=0\). Give a proof or counterexample for each of the following.
answered
Jan 31
in
Mathematics
|
242
views
invertible
matrices
proof
counterexample
1
answer
Let \(A\) be a square matrix. Proof or Counterexample. If \(A\) is diagonalizable, then so is \(A^{2}\).
answered
Jan 31
in
Mathematics
|
125
views
diagonalize
proof
counterexample
invertible
matrix
1
answer
Let \(A\) be a real square matrix satisfying \(A^{17}=0\).
answered
Jan 31
in
Mathematics
|
239
views
real
square
matrix
invertible
proof
counterexample
1
answer
A \(3 \times 3\) real matrix need not have any real eigenvalues.
answered
Jan 31
in
Mathematics
|
177
views
matrix
eigenvalue
real
square
invertible
complex
eigenvalues
1
answer
Let \(A\) be a square real (or complex) matrix. Then \(A\) is invertible if and only if zero is not an eigenvalue. Proof or counterexample.
answered
Jan 31
in
Mathematics
|
281
views
square
real
complex
matrix
invertible
eigenvalue
1
answer
Let \(A\) be a square real matrix all of whose eigenvalues are zero. Show that \(A\) is diagonalizable (that is, similar to a possibly comples diagonal matrix) if and only if \(A=0\).
answered
Jan 31
in
Mathematics
|
165
views
matrix
real
square
invertible
complex
eigenvalue
eigenvalues
1
answer
Let \(A\) be a square matrix of real numbers whose columns are (non-zero) orthogonal vectors.
answered
Jan 31
in
Mathematics
|
274
views
matrix
eigenvalue
real
invertible
square
complex
eigenvalues
1
answer
Give an example of a square real matrix that has rank 2 and all of whose eigenvalues are zero.
answered
Jan 31
in
Mathematics
|
159
views
matrix
real
square
invertible
complex
eigenvalue
eigenvalues
1
answer
A tridiagonal matrix is a square matrix with zeroes everywhere except on the main diagonal and the diagonals just above and below the main diagonal.
answered
Jan 31
in
Mathematics
|
199
views
matrix
eigenvalue
real
square
invertible
complex
eigenvalues
1
answer
What is a square matrix in mathematics?
answered
Jan 31
in
Mathematics
|
10
views
square
matrix
mathematics
1
answer
Interactive Content: Berry Info Wall
answered
Jan 31
in
Mathematics
|
4
views
interactive
content
berry
info
wall
quiz
2
answers
Synonyms of Mathematical Operators
answered
Jan 31
in
Mathematics
|
102
views
synonyms
mathematical
operators
1
answer
Solve the following equation and round your answer off to three decimal places: \[ 2^x=3 \]
answered
Jan 22
in
Mathematics
|
13
views
solve
equation
round
your
answer
decimal
places
1
answer
Simplify the following using the laws of logarithms:
answered
Jan 22
in
Mathematics
|
14
views
logarithms
grade12
expression
exponents
calculate
function
calculus
1
answer
Prove that \(\log _a x=\frac{\log _b x}{\log _b a}\)
answered
Jan 22
in
Mathematics
|
11
views
logarithms
exponents
prove
law
calculate
calculus
function
1
answer
Simplify \(\frac{\log 16}{\log 4}\)
answered
Jan 22
in
Mathematics
|
9
views
expression
logarithms
number
simplify
grade12
problem-solving
calculus
1
answer
SImplify \(\frac{\left(\log _2 8\right)^2}{\log _2 8^2}\)
answered
Jan 22
in
Mathematics
|
11
views
logarithms
expression
grade12
simplify
number
problem-solving
algebra
1
answer
simplify \(\log _3 \sqrt{27}\)
answered
Jan 22
in
Mathematics
|
11
views
expression
simplify
grade12
logarithms
problem-solving
exponents
calculate
1
answer
Simplify \(\log _3 \frac{1}{27}\)
answered
Jan 22
in
Mathematics
|
12
views
grade12
expression
simplify
logarithms
problem-solving
exponents
calculate
1
answer
simplify \(-\log 4-\log 25\)
answered
Jan 22
in
Mathematics
|
12
views
logarithms
expression
grade12
simplify
problem-solving
exponents
number
1
answer
simplify \(\log 20+\log 30-\log 6+\log _4 1\)
answered
Jan 22
in
Mathematics
|
12
views
calculate
expression
logarithms
grade12
exponents
function
calculus
1
answer
Simplify using laws of logs \(\log _3 27-\log _3 3\)
answered
Jan 22
in
Mathematics
|
12
views
logarithms
grade12
expression
exponents
simplify
problem-solving
calculate
1
answer
Simplify \(\log _9 27+\log _9 3\)
answered
Jan 22
in
Mathematics
|
11
views
expression
simplify
grade12
logarithms
problem-solving
exponents
1
answer
Prove that \(\log _a a=1\)
answered
Jan 22
in
Mathematics
|
14
views
logarithms
exponents
prove
law
calculate
function
calculus
1
answer
Using the laws of logarithms, expand \(\log _4\left(\frac{5}{x}\right)\)
answered
Jan 22
in
Mathematics
|
11
views
function
calculus
logarithms
calculate
exponents
grade12
expression
1
answer
Expand \(\log_{3}5x\)
answered
Jan 22
in
Mathematics
|
7
views
logarithms
exponents
function
expand
1
answer
Prove that \(\log _a x^m=m \log _a x \)
answered
Jan 22
in
Mathematics
|
17
views
prove
logarithms
exponents
law
calculate
function
calculus
1
answer
Prove that \(\log _a\left(\frac{x}{y}\right)=\log _a x-\log _a y \)
answered
Jan 22
in
Mathematics
|
14
views
logarithms
exponents
prove
law
function
calculus
calculate
1
answer
Prove that \(\log _a(x \times y)=\log _a x + \log _a y \)
answered
Jan 22
in
Mathematics
|
14
views
logarithms
exponents
law
prove
1
answer
Determine the domain of the function \(f(x)=\log _2(1-2 x)\).
answered
Jan 22
in
Mathematics
|
11
views
determine
domain
function
graph
intercepts
1
answer
The function \(f: x \rightarrow \log _a x\) passes through the point \((4 ;-2)\).
answered
Jan 22
in
Mathematics
|
19
views
equation
line
parallel
point
calculate
angle
collinear
1
answer
What is the inverse function of \(g(x)=\left(\frac{1}{2}\right)^x\)
answered
Jan 22
in
Mathematics
|
11
views
differential
function
equation
initial-conditions
point
bounded
continuity
1
answer
What is the inverse function of \(f(x)=\frac{1}{2} x+3\)?
answered
Jan 22
in
Mathematics
|
13
views
function
real
differentiable
open-set
subset
local
maximum
1
answer
What is the inverse function of \(f(x)=2 x-4\)?
answered
Jan 22
in
Mathematics
|
10
views
function
inverse
graph
domain
integral
sine
jee
1
answer
Define an inverse function
answered
Jan 22
in
Mathematics
|
15
views
function
inverse
differential
equation
initial-conditions
error
graph
1
answer
What is the horizontal line test for functions?
answered
Jan 22
in
Mathematics
|
9
views
vertical
functions
test
line
function
graph
horizontal
1
answer
What is the vertical line test for functions?
answered
Jan 22
in
Mathematics
|
11
views
vertical
line
test
functions
1
answer
If the time period of a simple pendulum is \(T=2 \pi \sqrt{l / g}\), then the fractional error in acceleration due to gravity is
answered
Jan 22
in
General Knowledge
|
92
views
time
period
simple
pendulum
fractional
error
1
answer
Solve $4^{ 1 / 2}$ exponent in the fractional form
answered
Jan 22
in
Mathematics
|
212
views
solve
exponent
equation
fractional
form
1
answer
What is fractional calculus?
answered
Jan 22
in
Mathematics
|
10
views
fractional
calculus
leibniz
1
answer
How do you find the domain and range of a function in interval notation?
answered
Jan 22
in
Mathematics
|
275
views
range
domain
function
graph
functions
interval
notation
1
answer
Are one-to-many relations considered as functions?
answered
Jan 22
in
Mathematics
|
10
views
one-to-many
relations
considered
domain
range
functions
1
answer
What is a many-to-one function?
answered
Jan 22
in
Mathematics
|
9
views
domain
range
many-to-one
function
1
answer
What is a one-to-one function?
answered
Jan 22
in
Mathematics
|
12
views
function
calculus
domain
range
1
answer
When doing image classification in Tensorflow, why do you scale the values to a range of 0 to 1 before feeding them to the neural network model?
answered
Jan 21
in
Data Science & Statistics
|
289
views
image
classification
tensorflow
scale
values
0
answers
In an arithmetic sequence \(S_n=n^2-2 n\). Use your formula in 2 to determine the value of:
asked
Jan 21
in
Mathematics
|
10
views
sequence
calculate
general
terms
sum
value
prove