FP3.6 - Further matrix algebra

Linear transformations of column Extension of work from FP1 to 3 dimensions. vectors in two and three dimensions and their matrix representation.

Use fp3.6.1 - linear transformations of column to connect the rule to the data and decision in the question.

This matters because fp3.6.1 - linear transformations of column determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.6.1 - linear transformations of column to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.6.1 - Linear transformations of column is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Combination of transformations.; The transformation represented by AB is the transformation Products of matrices. represented by B followed by the transformation represented by A.

Use fp3.6.2 - combination of transformations to connect the rule to the data and decision in the question.

This matters because fp3.6.2 - combination of transformations determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.6.2 - combination of transformations to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.6.2 - Combination of transformations is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Transpose of a matrix.; Use of the relation (AB)T = BTAT.

Use fp3.6.3 - transpose of a matrix to connect the rule to the data and decision in the question.

This matters because fp3.6.3 - transpose of a matrix determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.6.3 - transpose of a matrix to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.6.3 - Transpose of a matrix is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Evaluation of 3 × 3 determinants.; Singular and non-singular matrices.

Use fp3.6.4 - evaluation of 3 × 3 determinants to connect the rule to the data and decision in the question.

This matters because fp3.6.4 - evaluation of 3 × 3 determinants determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.6.4 - evaluation of 3 × 3 determinants to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.6.4 - Evaluation of 3 × 3 determinants is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Inverse of 3 × 3 matrices.; Use of the relation (AB)−1 = B−1A−1.

Use fp3.6.5 - inverse of 3 × 3 matrices to connect the rule to the data and decision in the question.

This matters because fp3.6.5 - inverse of 3 × 3 matrices determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.6.5 - inverse of 3 × 3 matrices to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.6.5 - Inverse of 3 × 3 matrices is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The inverse (when it exists) of a given transformation or combination of transformations.

Use fp3.6.6 - inverse transformations and combinations to connect the rule to the data and decision in the question.

This matters because fp3.6.6 - inverse transformations and combinations determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.6.6 - inverse transformations and combinations to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.6.6 - Inverse transformations and combinations is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Eigenvalues and eigenvectors of Normalised vectors may be required. 2 × 2 and 3 × 3 matrices.

Use fp3.6.7 - eigenvalues and eigenvectors to connect the rule to the data and decision in the question.

This matters because fp3.6.7 - eigenvalues and eigenvectors determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.6.7 - eigenvalues and eigenvectors to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.6.7 - Eigenvalues and eigenvectors is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Reduction of symmetric matrices to Students should be able to find an orthogonal matrix P such diagonal form. that PTAP is diagonal.

Use fp3.6.8 - reduction of symmetric matrices to connect the rule to the data and decision in the question.

This matters because fp3.6.8 - reduction of symmetric matrices determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp3.6.8 - reduction of symmetric matrices to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP3.6.8 - Reduction of symmetric matrices is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.