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Matrices, GEN1 2024 NHT 27 MC

Matrix \(V\) is an  \(n \times n\)  matrix with a determinant equal to 1 .

The product of \(V \times V^{-1}\) will result in

  1. an identity matrix.
  2. a Leslie matrix.
  3. a column matrix.
  4. a zero matrix.
  5. a row matrix.
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\(A\)

Show Worked Solution

\(\text{Since matrix determinant}\ \neq 0\ \ \Rightarrow\ \ \text{matrix has an inverse}\)

\(\therefore V \times V^{-1} = I\)

\(\Rightarrow A\)

MATRICES, FUR2 2020 VCAA 2

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

`[(5, -9),(4, -7)][(x),(y)]=[(7), (6)]`
 

  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)

 
`[(text( __), 9),(text( __), text( __)\ )]`
 

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

Show Answers Only
  1. `text(S) text(ince determinant) = 1 != 0,`

     

    `text(the matrix has an inverse)`

  2. `[(-7, 9),(-4, 5)]`
  3. `2`
Show Worked Solution

a.  `text(S) text(ince determinant) = 1 != 0,`

♦ Mean mark part (a) 37%.

`->\ text(the matrix has an inverse)`


b.  `[(-7, 9),(-4, 5)]`

 

Mean mark part (c) 51%.
c.   `[(x), (y)] = [(-7, 9), (-4, 5)][(7), (6)] = [(7),(2)]`

 
`:.\ text(Preferred number of sandwich bars) = 2`