SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Matrices, GEN1 2022 VCAA 5 MC

Matrix is a 2 × 2 matrix.

Matrix is a 2 × 3 matrix.

Matrix is a 3 × 2 matrix.

Matrix is a 3 × 3 matrix.

Which one of the following matrix products could have an inverse?

Show Answers Only

Show Worked Solution

Matrix product requires: [m × n] × [n × m]

Matrix inverse requires a square matrix: [m × n] × [m × n] = [m × m]

Option A:  = [2 × 2] × [2 × 3] → [2 × 3]  (not square, eliminate A)

Option B:  = [2 × 3] × [3 × 3] → [2 × 3]  (not square, eliminate B)

Option C:  = [3 × 2] × [2 × 2] → [3 × 2]  (not square, eliminate B)

Option D:  = [3 × 2] × [2 × 3] → [3 × 3]  (correct)

Option E:  = [3 × 3] × [3 × 2] → [3 × 2]  (not square, eliminate E)

MATRICES, FUR1 2011 VCAA 9 MC

Matrix  is a 3 x 3  matrix. Seven of the elements in matrix  are zero.

Matrix  contains six elements, none of which are zero.

Assuming the matrix product    is defined, the minimum number of zero elements in the product matrix    is

A.   

B.   

C.   

D.   

E.   

Show Answers Only

Show Worked Solution