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Mathematics Grade 11 Unit 4: DETERMINANTS AND THEIR PROPERTIES

national exam questions have come from this unit. It runs 42 pages; one careful study pass takes about 4.4 hours, and its difficulty is harder among Mathematics units. Each section below lists the questions set from it, with the year, and opens the page that teaches it.

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4.1 Determinants of Matrices of Order · read p. 209
Not asked in a national paper yet.
4.2 Minors and Cofactors of Elements of Matrices · read p. 211
  • 2018 E.C., Q44 – Let AA be a 3×3 invertible matrix with determinant |A|=4. What is the determinant of ?
  • 2018 E.C., Q26 – If $A = \begin{pmatrix}3 & 1 & 1 \ 2 & -1 & 1 \ 0 & 1 & 3\end{pmatrix}$, then what is the value of $\det(A)$?
  • 2018 E.C., Q21 – What is the transpose of the matrix $M=\begin{pmatrix}1&2&1\0&-1&3\2&1&5\end{pmatrix}$?
  • 2018 E.C., Q43 – If AA is a 3×3 square matrix, which of the following is always true about its transpose AT? det(A ) = T −det(A) det(A ) = T 1/det(A)
  • 2018 E.C., Q16 – Let a matrix $A = \begin{pmatrix} 1 & -3 & 2 \\ -3 & 3 & -1 \\ 2 & -1 & 0 \end{pmatrix}$. Then what is the inverse of A?
  • 2017 E.C., Q36 – What is the determinant of the matrix $\begin{pmatrix}\frac{1}{2} & 1 & \frac{3}{2} \ 2 & \frac{5}{2} & 3 \ \frac{7}{2} & 4 & \frac{9}{2}\end{pmatrix}$?
  • 2017 E.C., Q4 – Consider the matrix $\begin{pmatrix} 2 & -3 & 1 \\ 0 & -1 & \pi \\ 3 & 1 & 4 \end{pmatrix}$. What is the cofactor of entry $\pi$?
  • 2016 E.C., Q16 – Which one of the following numbers is the determinant of the matrix $M = \begin{pmatrix}1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 10\end{pmatrix}$?
  • 2015 E.C., Q16 – Let $M=\begin{pmatrix}-\frac{1}{2}&\frac{1}{2}\[2pt]\frac{1}{2}&-\frac{1}{2}\end{pmatrix}$ and $Q=\begin{pmatrix}1&-1\-1&1\end{pmatrix}$ be given matrices. Which one of the following is true?
  • 2015 E.C., Q15 – Which one of the following is true about the determinant of a matrix?
  • 2014 E.C., Q48 – Which one of the following is true about the matrix $ \begin{pmatrix} 1 & 3 & 5 \\ 6 & 4 & 2 \\ 9 & 7 & 0 \end{pmatrix} $?
  • 2014 E.C., Q37 – If A is a 3 × 3 matrix with det(A) = 5, then what is the determinant of 2A?
  • 2013 E.C., Q11 – What is the determinant of the matrix $\begin{bmatrix} 1 & -7 \\ 6 & 5\end{bmatrix}$?
  • 2013 E.C., Q19 – Which one of the following is NOT true about the determinant of a given square matrix A?
4.3 Determinants of Matrices of Order · read p. 211
Not asked in a national paper yet.
4.4 Properties of Determinants · read p. 211
Not asked in a national paper yet.
4.5 Inverse of a Square Matrix of Order 2 and · read p. 230
  • 2017 E.C., Q21 – Which of the following matrix is the inverse of the matrix $\begin{pmatrix}1&-1&2\1&0&1\3&1&3\end{pmatrix}$?
4.6 Solutions of Systems of Linear Equations Using Cramer’s Rule · read p. 235
  • 2017 E.C., Q45 – Which one of the following systems of equations possesses no solution?
  • 2016 E.C., Q24 – Given the linear system, $\begin{cases}a_1x+b_1y+c_1z=3\a_2x+b_2y+c_2z=-1\a_3x+b_3y+c_3z=2\end{cases}$, such that the determinant of the coefficient matrix is $\frac{1}{3}$. Which of the following is the value of y?
  • 2016 E.C., Q4 – The solution set of the system $\begin{cases} 2x - y = 5 \\ 3y + 15 = 6x \end{cases}$ is:
  • 2015 E.C., Q22 – Which one of the following is true about the system of linear equations $$\left\{ \begin{aligned} 3x + y - z &= 1 \\ 2x - y + 2z &= 2 \\ -x + y + z &= -1 \end{aligned} \right.$$
  • 2013 E.C., Q21 – Consider the system of linear equation $ \left\{ \begin{array}{r l} 3x - ay & = 1 \\ 6x + 4y & = 5 \end{array} \right. $ Then which of the following is true?
4.7 Applications · read p. 242
Not asked in a national paper yet.