Ask a math question of medium difficulty. Try looking through some and see if you can work out the answers. You'll need a writing utensil and some paper. Don't be lazy.
Here are two problems to get things started:
(Without looking in your book) Give an example of two $2\times 2$ matrices which do not commute.
If there was a $2\times 2$ matrix $A$ such that $A \cdot B = B \cdot A $ for all $2\times 2$ matrices $B$, what does $A$ look like?
Interpret the following Leslie Matrix.
ReplyDelete0 5 2.5 0
.8 0 0 0
0 .5 0 0
0 0 .1 0
Then find the next three population vectors if the starting population N0(t) is 1000, the next generation at the start of the breeding season is N1(t)=800, the start of the next breeding season is N2(t)=500, and the start of the next breeding season is N3(t)=100
Interpret the following Leslie Matrix.
Delete$\begin{bmatrix} 0 &5 &2.5& 0\\
.8& 0& 0& 0\\
0 &.5 &0& 0\\
0& 0& .1& 0 \end{bmatrix}$
Then find the next three population vectors if the starting population $N_0(t)=1000$, the next generation at the start of the breeding season is $N_1(t)=800$, the start of the next breeding season is $N_2(t)=500$, and the start of the next breeding season is $N_3(t)=100$
(see example 17 in section 9.2 on page 462 )
A is represented by the Matrix
ReplyDelete5 6
7 10
and B is represented by the Matrix
8 9 13 12
6 3 10 -8
If AX=B solve for the Matrix X.
Next keep B the same but change A to the matrix
3 6
2 4
$A$ is represented by the matrix $\begin{bmatrix} 5 &6 \\ 7 &10\end{bmatrix}$
Deleteand $B$ is represented by the matrix $\begin{bmatrix} 8& 9& 13& 12\\ 6& 3& 10& -8\end{bmatrix}$
Is there a solution to $AX=B$, if so, solve for the matrix $X$.
Next keep $B$ the same but change $A$ to the matrix
$\begin{bmatrix} 3& 6 \\ 2 &4 \end{bmatrix}$.
Is there a solution to $AX=B$, if so, solve for the matrix $X$.
Find the inverse of the 2x2 matrix B if B equals:
ReplyDelete2 4
1 4
What is the determinant of this 3x3 matrix?
ReplyDelete3 4 1
6 8 2
5 7 9
If $\left| \vec{x} \right| = 5$, what is the length of $-3 \vec{x}$?
ReplyDeleteFind A^3 if
ReplyDeleteA =
3 -1
4 7
Find the values of x, y, and z that satisfy all three equations:
ReplyDelete3x + 5y - z = 10
2x - y + 3z = 9
4x + 2y - 3z = -1
Find A^2 x C' for the following matrices
ReplyDeleteA= 2 5 B= 1 4 C= 6 2
3 8 7 4 5 3
4 1
Given $A= \begin{bmatrix}2& 5\\3&8\end{bmatrix}$ $B= \begin{bmatrix}1 &4\\7&4\end{bmatrix}$ $C= \begin{bmatrix}6& 2\\5&3\end{bmatrix}$, determine $A^2 C$.
DeleteGiven the following matrix A, find its eigenvalues and corresponding eigenvectors.
ReplyDelete4 3
1 5
Show that AB =/= BA if
ReplyDeleteA=
3 5
-3 2
and
B=
5 9
2 -1
Given $A=\begin{bmatrix} 3 & 5\\ -3 & 2 \end{bmatrix}$ and $B=\begin{bmatrix} 5&9\\2&-1 \end{bmatrix}$, show that $AB \neq BA$.
DeleteLaboratory mice are fed with a mixture of two foods that contain two essential nutrients. food 1 contains 3 units of nutrient A and 2 units of nutrient B per ounce; food 2 contains 4 units of nutrient A and 5 units of nutrient B per ounce. In what proportion should you mix the food if the mice require nutrients A and B in equal amounts?
ReplyDeleteShow that (AB)' does not equal A'B'
ReplyDeleteLet A = 4 1 3
0 1 2
1 0 0
Let B= 1 0 1
2 3 1
5 1 0
Find the inverse of the following 3x3 matrix:
ReplyDelete9 4 1
A= 0 2 3
5 8 0
find [ A^-1 + B ] C
ReplyDeleteWhere:
A=2 5
7 5
B= 3 1
2 5
C=1 0
3 0
Find the eigenvalues and eigenvectors for the following matrix:
ReplyDeleteA= [3 6]
[2 8]
Find the eigenvalues of matrix (AB)'
ReplyDeleteWhere
A = [7 5 ]
6 9
B = [3 5]
5 1
find and classify the equlibria points when dy/dx = X^3+4x^2+2x
ReplyDeleteI will adjust this problem to being:
DeleteFind and classify the equilibria to
$\frac{dy}{dx}=y^3+4y^2+4y$
Vector A and Vector B are represented by the Cartesian system as (3, 4) and (1/2, 3) respectively. The vectors are added. Define Vector(A+B) using polar coordinates.
ReplyDeleteANSWER THESE QUESTIONS:
ReplyDeleteNormalize this vector: [1, 5, 12]
Find the dot product of (2, 1) (5, 6)
Find the angle between these 2 lines: x = [-1,2]' y = [-2,-4]'
-Seal-Bin Han
Let A =
ReplyDelete2 3
1 4
Find (A^12)X for
x =
6
4
Everyone should know how to do this.
DeleteCompute $A^{12} x$ where $A=\begin{bmatrix} 2&3\\1&4\end{bmatrix}$ and $x=\begin{bmatrix} 6\\ 4\end{bmatrix}$
Find [A+B]^-1
ReplyDeletewhen A= 5 7
2 4
and B = 2 1
3 4
Calculate the value of the following integral with the bounds of negative infinity to positive infinity ∫ (1/(x^2 -1) dx
ReplyDeleteDoes $\int_{-\infty} ^{\infty} \frac{1}{x^2-1}dx$ exist?
DeleteFind the eigenvalues and eigenvectors for martrix G.
ReplyDeleteG=
[3 6]
[2 4]