diff --git a/source/linear-algebra/source/01-LE/01.ptx b/source/linear-algebra/source/01-LE/01.ptx index a2c54d722..9b0099eed 100644 --- a/source/linear-algebra/source/01-LE/01.ptx +++ b/source/linear-algebra/source/01-LE/01.ptx @@ -508,7 +508,7 @@ system). Otherwise it is inconsistent.inconsistent linear s
Intersection of three planes at one point - + @@ -516,7 +516,7 @@ system). Otherwise it is inconsistent.inconsistent linear s

Three planes are shown to intersect at a single point. An arrow points to the point of intersection at coordinates (1,2,3).

- + @@ -528,7 +528,7 @@ system). Otherwise it is inconsistent.inconsistent linear s
Intersection of three planes at a line - + @@ -536,7 +536,7 @@ system). Otherwise it is inconsistent.inconsistent linear s

Three planes are shown to intersect along a line of points.

- + @@ -548,7 +548,7 @@ system). Otherwise it is inconsistent.inconsistent linear s
Three non-mutually-intersecting planes - + @@ -556,7 +556,7 @@ system). Otherwise it is inconsistent.inconsistent linear s

Three planes are shown to intersect at no common point, although each pair of planes intersects along a line of points.

- + diff --git a/source/linear-algebra/source/02-EV/01.ptx b/source/linear-algebra/source/02-EV/01.ptx index e09a7399a..c5ab6ec6a 100644 --- a/source/linear-algebra/source/02-EV/01.ptx +++ b/source/linear-algebra/source/02-EV/01.ptx @@ -221,27 +221,26 @@ we refer to this real number as a scalar.

-

- Correct the SageMath code cell below to generate - an illustration of several vectors belonging to - \vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right], - \left[\begin{array}{c}-1\\1\end{array}\right]\right\}= - \setBuilder{a\left[\begin{array}{c}1\\2\end{array}\right]+ - b\left[\begin{array}{c}-1\\1\end{array}\right]}{a, b \in \IR} - in the xy plane. -

- - - - - -

- Based on this illustration, which of these geometrical objects - best describes the span of these two vectors? +

+ In addition to the combinations above, use the interactive below to graph an additional + 5 or more vectors belonging to + \vspan\left\{\left[\begin{array}{c}1\\2\end{array}\right], + \left[\begin{array}{c}-1\\1\end{array}\right]\right\}= + \setBuilder{a\left[\begin{array}{c}1\\2\end{array}\right]+ + b\left[\begin{array}{c}-1\\1\end{array}\right]}{a, b \in \IR} + in the xy plane.

-

- Which of these geometrical objects - best describes the span of these two vectors? + + + + + +

An interactive that graphs linear combinations of the vectors \left[\begin{array}{c}1\\2\end{array}\right] and + \left[\begin{array}{c}-1\\1\end{array}\right].

+ + +

+ Which of these geometrical objects best describes the span of these two vectors?

  1. A line
  2. diff --git a/source/linear-algebra/source/02-EV/doenet/EV1-span-two-vectors.xml b/source/linear-algebra/source/02-EV/doenet/EV1-span-two-vectors.xml new file mode 100644 index 000000000..cfaf9f54e --- /dev/null +++ b/source/linear-algebra/source/02-EV/doenet/EV1-span-two-vectors.xml @@ -0,0 +1,59 @@ +

    + Enter several pairs of coefficients (a,b), separated by commas: + +

    + + + (1,2) + (-1,1) + $in + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Graph of two vectors and linear combinations thereof + + + + + + +