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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?

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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, FUR2 2020 VCAA 2

The preferred number of cafes and sandwich bars in Grandmall’s food court can be determined by solving the following equations written in matrix form.
 


 

  1. The value of the determinant of the 2 × 2 matrix is 1.
  2. Use this information to explain why this matrix has an inverse.   (1 mark)

  3. Write the three missing values of the inverse matrix that can be used to solve these equations.   (1 mark)

 

 

  1. Determine the preferred number of sandwich bars for Grandmall’s food court.   (1 mark)

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  1.  

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a. 

♦ Mean mark part (a) 37%.


b. 

 

Mean mark part (c) 51%.
c.