Content location → Linear transformationsEvidenceHere the real matrices represent linear maps in standard column-vector coordinates. A∘B means applying B first and A second, so its representing matrix is AB. The circle is composition, not entrywise multiplication.
Content location → Linear transformationsEvidenceConnection evidence is not yet available in this language.
Content location → MatricesEvidenceTo construct the matrix of A∘B, take each column of B as an input vector and apply A to it. The resulting image becomes the corresponding column of A∘B. The video illustrates this by matching the known first and third columns with colored ovals.
Content location → MatricesEvidenceConnection evidence is not yet available in this language.
Explanation → Linear transformationsEvidenceHere the real matrices represent linear maps in standard column-vector coordinates. A∘B means applying B first and A second, so its representing matrix is AB. The circle is composition, not entrywise multiplication.
Explanation → Linear transformationsEvidenceConnection evidence is not yet available in this language.
Content location → Composing 3x3 matrices | Matrices | Precalculus | Khan AcademyEvidenceHere the real matrices represent linear maps in standard column-vector coordinates. A∘B means applying B first and A second, so its representing matrix is AB. The circle is composition, not entrywise multiplication.
Explanation → Linear transformationsEvidenceHere the real matrices represent linear maps in standard column-vector coordinates. A∘B means applying B first and A second, so its representing matrix is AB. The circle is composition, not entrywise multiplication.
Explanation → MatricesEvidenceTo construct the matrix of A∘B, take each column of B as an input vector and apply A to it. The resulting image becomes the corresponding column of A∘B. The video illustrates this by matching the known first and third columns with colored ovals.
Explanation → MatricesEvidenceConnection evidence is not yet available in this language.
Content location → Composing 3x3 matrices | Matrices | Precalculus | Khan AcademyEvidenceTo construct the matrix of A∘B, take each column of B as an input vector and apply A to it. The resulting image becomes the corresponding column of A∘B. The video illustrates this by matching the known first and third columns with colored ovals.
Explanation → MatricesEvidenceTo construct the matrix of A∘B, take each column of B as an input vector and apply A to it. The resulting image becomes the corresponding column of A∘B. The video illustrates this by matching the known first and third columns with colored ovals.
math