diff --git a/source/linear-algebra/source/01-LE/01.ptx b/source/linear-algebra/source/01-LE/01.ptx index 9d148bbc8..a2c54d722 100644 --- a/source/linear-algebra/source/01-LE/01.ptx +++ b/source/linear-algebra/source/01-LE/01.ptx @@ -253,7 +253,7 @@ Following are some examples of addition and scalar multiplication in \mathbb

- Visualization of adding vectors + Visualization of scaling vectors @@ -1135,8 +1135,8 @@ Augmented matrix:

For each of the following relations, show that it is or is not an equivalence relation.

    -
  • For a,b, \in \mathbb{R}, a \sim b if an only if a \leq b.
  • -
  • For a,b, \in \mathbb{R}, a \sim b if an only if |a|=|b|.
  • +
  • For a,b, \in \mathbb{R}, a \sim b if and only if a \leq b.
  • +
  • For a,b, \in \mathbb{R}, a \sim b if and only if |a|=|b|.

diff --git a/source/linear-algebra/source/01-LE/02.ptx b/source/linear-algebra/source/01-LE/02.ptx index 98e0ad1b3..d7f1873ca 100644 --- a/source/linear-algebra/source/01-LE/02.ptx +++ b/source/linear-algebra/source/01-LE/02.ptx @@ -232,7 +232,7 @@ Multiply a row by a nonzero constant, for example: \left[\begin{array}{cc|c} 1 & 2 & 4 \\ 1 & 3 & 5 \end{array}\right] \sim - \left[\begin{array}{cc|c} 3(1) & 3(2) & 3(4) + \left[\begin{array}{cc|c} (3)1 & (3)2 & (3)4 \\ 1 & 3 & 5 \end{array}\right]

@@ -423,7 +423,7 @@ solution set? \left[\begin{array}{cc|c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}\right] \sim - \left[\begin{array}{cc|c} 2(1) & 2(2) & 2(3) \\ 4 & 5 & 6 \end{array}\right] + \left[\begin{array}{cc|c} (2)1 & (2)2 & (2)3 \\ 4 & 5 & 6 \end{array}\right]

@@ -432,7 +432,7 @@ solution set? \left[\begin{array}{cc|c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}\right] \sim - \left[\begin{array}{cc|c} 1 & 2 & 3 \\ 4-4(1) & 5-4(2) & 6-4(3) \end{array}\right] + \left[\begin{array}{cc|c} 1 & 2 & 3 \\ 4-(4)1 & 5-(4)2 & 6-(4)3 \end{array}\right]