Further Mathematics

I am in SS 3. Set me a scalar multiplication question like A=[[0,-4,1],[2,1,-2],[3,0,5]],

Explain in simple terms why AB is not usually equal to BA for matrices, using a worked 2x2

Explain what the identity matrix I is and show, with a 3x3 numerical example, that AI = IA

I am in SS 3. Explain the zero matrix and its effect in addition, using a 2x2 example to s

Give me a 2x2 matrix like A=[[-3,2],[4,-5]] and ask me to evaluate its determinant using a

Give me a 3x3 matrix like A=[[2,0,-1],[3,1,2],[-1,4,0]] and ask me to evaluate its determi

Explain the checkerboard pattern of positive and negative signs used when expanding a 3x3

Quiz me with two questions, one 2x2 determinant and one 3x3 determinant, mark both, and te

Give me a Cambridge Additional Mathematics style 3x3 determinant question that says 'show

Use Cramer's rule to solve 5x + 2y = 16 and x - 3y = -7. Set up the coefficient determinan

Give me a 2x2 matrix like A=[[2,3],[1,4]] and ask me to find its inverse using the determi

Give me a 2x2 matrix like A=[[3,2],[5,4]] and ask me to find its inverse using the determi

Explain what the adjoint of a matrix is and how it relates to the matrix of cofactors, usi

I am in SS 3. Explain why a matrix cannot be inverted when its determinant is zero, and gi

I found the inverse of a 2x2 matrix but I think I mixed up the sign or swapped the wrong d

You are my SS3 Further Mathematics tutor. Teach me the determinant of a three by three mat

Show me how to solve the system x+y+z=6, 2x-y+z=3, x+2y-z=2 by writing it as AX=B, finding

Quiz me on the SI unit of force and how it is derived from mass and acceleration, then giv

I am in SS 3. Teach me the difference between mass, force and weight from scratch, as if I

Give me a problem with two forces of 5N and 9N acting at 45 degrees and ask me to find the