VECTORS AND MATRICES

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You should be able to

 

 explain concepts associated with vectors;

 

Concept of a vector, magnitude, direction, line segment, scalar.

 

 combine vectors;

 

Triangle law, or parallelogram laws 2x1 Column matrices,

 

 express a point P(a,b) as a position vector

 

 

where O is the origin (0, 0)

Displacement and position vectors; co-ordinates.

 

 

 determine the magnitude of a vector;

 

Including unit vectors.

 

 

 use vectors to solve problems in Geometry;

 

Collinearity, parallel.

 

 

 explain concepts associated with matrices;

 

Concept of a matrix, row, column, order, types of matrices, practical use.

 

 

 perform addition, subtraction and multiplication of matrices and multiplication of matrices by a scalar;

 

 

Non-commutativity of matrix multiplication.

 

 evaluate the determinant of a 2 x 2 matrix;

 

 solve problems involving a 2 x 2 singular matrix;

 

 obtain the inverse of a non-singular „2 x 2‟ matrix;

 

Determinant and adjoint of a matrix.

 determine a „2 x 2‟ matrix representation of the single transformation which is equivalent to the composition of two linear transformations in a plane (where the origin remains fixed);