Given $6$ vectors in $\mathbb{R^4}$ and given that they span $\mathbb{R^4}$ find a  basis.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=1-\sin(y)$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point. 

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x)-\sin(y)$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point. 

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

This exercise will help you solve questions based on subduction zones using  the Cosine rule.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=\sin(x-y)$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point. 

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^3-y^3$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

angle between two vectors

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Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Vector addition, multiplication by a scalar, magnitude, dot product, Perpendicular vectors, angle between vectors, cross product.

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Given two ordered sets of vectors $S,\;T$ in $\mathbb{R^5}$ find the reduced echelon form of the matrices given by $S$ and $T$ and hence determine whether or not they span the same subspace.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Find eigenvalues and eigenvectors of a $2 \times 2$ matrix.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Gitt vektorene  $\boldsymbol{A,\;B}$, finn vinkelen mellom dem.

Question 5 of CBA1;  Testing vector operations.

Given the vector equations of two straight lines, find the coordinates of the point of intersection

Given the vector equations of two straight lines, find the angle between them