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Mathematics Grade 11 Unit 3: MATRICES

national exam questions have come from this unit. It runs 77 pages; one careful study pass takes about 8.2 hours, and its difficulty is moderate 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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3.1 The Concepts of a Matrix · read p. 133
  • 2018 E.C., Q16 – Consider the matrix $A=\begin{pmatrix}-1&2&1\3&4&2\1&1&5\end{pmatrix}$. Which of the following statements is true about the minor of the entries of A?
  • 2018 E.C., Q54 – Which one of the following statements defines a matrix?
3.2 Operations on Matrices · read p. 137
  • 2018 E.C., Q42 – Which of the following properties of matrices and scalar multiplication r is TRUE for any two matrices A and B of the same dimension?
  • 2017 E.C., Q41 – If $\begin{pmatrix}x+y&2\5&3\end{pmatrix}=\begin{pmatrix}7&2\5&x-y\end{pmatrix}$, then what is the value of $x$?
  • 2014 E.C., Q11 – Let A = $A=\begin{pmatrix}0&-1\\5&1\end{pmatrix}$ Which one of the following is equal to A+A T ?
  • 2014 E.C., Q10 – A −B Given matrices and . Which one of the following is ?
  • 2014 E.C., Q12 – Given matrices \( A = \begin{pmatrix} 2 & 0 & 5 \\ 3 & 1 & 4 \\ 0 & 6 & -2 \end{pmatrix} \) and \( B = \begin{pmatrix} 1 & 3 & 0 \\ 6 & 5 & 2 \\ 9 & 7 & 0 \end{pmatrix} \). Which one of the following is \( A - B \)?
  • 2013 E.C., Q18 – Which of the following is the product $AB$ of the two matrices $A=\begin{bmatrix}-2 & 3\\ 1 & 4\end{bmatrix}$ and $B=\begin{bmatrix}-1 & 5\\ 3 & 0\end{bmatrix}$?
3.3 Special Types of Matrices · read p. 157
  • 2018 E.C., Q30 – Which one of the following is a skew symmetric matrix?
3.4 Elementary Row Operations of Matrices · read p. 163
  • 2017 E.C., Q40 – What is the inverse of the matrix $\begin{pmatrix} -2 & 1 \\ 0 & 3 \end{pmatrix}$?
  • 2016 E.C., Q38 – M 3 2 Let be a matrix such that . Which one of the following matrices is equal to ? 0 3 6 −8 8 6 9 4 10 6 −8 16 12 18 4 10
3.5 Systems of Linear Equations with Two or Three Variables · read p. 174
Not asked in a national paper yet.
3.6 Solutions of Systems of Linear Equations · read p. 182
  • 2018 E.C., Q21 – Consider the following system of linear equations. $\begin{cases}x-y=2\3x+y=4\2x-2y=3\end{cases}$ Then which one of the following matrices is the reduced form of the augmented matrix into triangular matrix?
  • 2017 E.C., Q28 – Which of the following statement is true about the given system of linear equations?
  • 2017 E.C., Q47 – The system of linear equations $\begin{cases} x + z = 0 \\ 2x + y = 1 \\ x + 2y + z = 0 \end{cases}$ in matrix form is equal to:
  • 2016 E.C., Q39 – Which of the following pairs of lines with the given equations are parallel?
  • 2015 E.C., Q9 – Which of the following is the solution set of the equation $\frac{3}{x + 1} - \frac{1}{x - 1} = \frac{2}{x}$?
  • 2014 E.C., Q45 – Which one of the following is the augmented matrix associated to the system of equations: $$\left\{ \begin{aligned} 2x + y + 3z & = 4 \\ x - z & = 1 \\ -4x + y & = 3 \end{aligned} \right.$$
3.7 Inverse of a Square Matrix · read p. 192
  • 2017 E.C., Q10 – For what value of $x$ is the matrix $\begin{pmatrix} 1 & 0 & 1 \\ 2x+1 & 3 & 0 \\ 1 & -1 & x \end{pmatrix}$ invertible?
  • 2013 E.C., Q20 – Which of the following is the inverse of the matrix $\begin{bmatrix}2 & 3\\ 3 & 4\end{bmatrix}$?
3.8 Applications · read p. 199
  • 2014 E.C., Q35 – Let $A=\begin{pmatrix}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{pmatrix}$ and det(A)=3. Which one of the following is NOT true?