MathAmigo

Matrices

Secondary 4 practice

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Matrices practice questions

Secondary 4 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Matrix A=(−62−5−44568−1)A = \begin{pmatrix} -6 & 2 & -5 \\ -4 & 4 & 5 \\ 6 & 8 & -1 \end{pmatrix}. Find the element in row 3, column 2.
Show the worked solution
  • We need the element in row 33, column 22, of matrix AA.
  • Row 33 of AA: (68−1)\begin{pmatrix} 6 & 8 & -1 \end{pmatrix}
  • The 2nd entry in this row is 88.
  • So the element in row 3, column 2, is 88.

Answer: 88

Example 2

Given A=(9−13311)A = \begin{pmatrix} 9 & -1 & 3 \\ 3 & 1 & 1 \end{pmatrix} and B=(7−18−435)B = \begin{pmatrix} 7 & -1 & 8 \\ -4 & 3 & 5 \end{pmatrix}, find A+BA + B.
Show the worked solution
  • A+B=(9−13311)+(7−18−435)add corresponding elementsA + B = \begin{pmatrix} 9 & -1 & 3 \\ 3 & 1 & 1 \end{pmatrix} + \begin{pmatrix} 7 & -1 & 8 \\ -4 & 3 & 5 \end{pmatrix} \quad \scriptsize\textit{add corresponding elements}
  • =(9+(7)−1+(−1)3+(8)3+(−4)1+(3)1+(5))= \begin{pmatrix} 9+(7) & -1+(-1) & 3+(8) \\ 3+(-4) & 1+(3) & 1+(5) \end{pmatrix}
  • =(16−211−146)= \begin{pmatrix} 16 & -2 & 11 \\ -1 & 4 & 6 \end{pmatrix}

Answer: 16,−2,11,−1,4,616,-2,11,-1,4,6

Example 3

Given A=(2−333)A = \begin{pmatrix} 2 & -3 \\ 3 & 3 \end{pmatrix} and B=(023−1)B = \begin{pmatrix} 0 & 2 \\ 3 & -1 \end{pmatrix}, evaluate −2A+5B-2A + 5B.
Show the worked solution
  • (−2)A=(−46−6−6)(-2)A = \begin{pmatrix} -4 & 6 \\ -6 & -6 \end{pmatrix}
  • 5B=(01015−5)5B = \begin{pmatrix} 0 & 10 \\ 15 & -5 \end{pmatrix}
  • −2A+5B=(−46−6−6)+(01015−5)-2A + 5B = \begin{pmatrix} -4 & 6 \\ -6 & -6 \end{pmatrix} + \begin{pmatrix} 0 & 10 \\ 15 & -5 \end{pmatrix}
  • −2A+5B=(−4169−11)-2A + 5B = \begin{pmatrix} -4 & 16 \\ 9 & -11 \end{pmatrix}

Answer: −4,16,9,−11-4, 16, 9, -11

Questions parents ask

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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