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Dear Students,
Welcome to today’s quiz! This is your opportunity to demonstrate what you’ve learned so far, so do your best. Please keep in mind that you have a maximum of 60 minutes to complete all the questions. Make sure to manage your time wisely and answer each question thoughtfully.
Good luck!
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Pertanyaan 1 dari 13
1. Pertanyaan
1 pointsJika \(A = \begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix}\) dan \(I\) matriks satuan ordo 2, maka \(A^2 \:-\:2A + 6I = \dotso\)
Benar
\(\begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix}\cdot \begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix} \cdot \begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix}\:-\:2\begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix} + 6\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\)
\(\begin{bmatrix}1 & 0 \\-8 & 9 \end{bmatrix}\cdot \begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix}\:-\:\begin{bmatrix}2 & 0 \\-4 & 6 \end{bmatrix} + \begin{bmatrix}6 & 0 \\0 & 6\end{bmatrix}\)
\(\begin{bmatrix}1 & 0 \\-26 & 27 \end{bmatrix}\:-\:\begin{bmatrix}2 & 0 \\-4 & 6 \end{bmatrix} + \begin{bmatrix}6 & 0 \\0 & 6 \end{bmatrix}\)
\(\begin{bmatrix}5 & 0 \\-22 & 27 \end{bmatrix}\)
Salah
\(\begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix}\cdot \begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix} \cdot \begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix}\:-\:2\begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix} + 6\begin{bmatrix}1 & 0 \\0 & 1 \end{bmatrix}\)
\(\begin{bmatrix}1 & 0 \\-8 & 9 \end{bmatrix}\cdot \begin{bmatrix}1 & 0 \\-2 & 3 \end{bmatrix}\:-\:\begin{bmatrix}2 & 0 \\-4 & 6 \end{bmatrix} + \begin{bmatrix}6 & 0 \\0 & 6\end{bmatrix}\)
\(\begin{bmatrix}1 & 0 \\-26 & 27 \end{bmatrix}\:-\:\begin{bmatrix}2 & 0 \\-4 & 6 \end{bmatrix} + \begin{bmatrix}6 & 0 \\0 & 6 \end{bmatrix}\)
\(\begin{bmatrix}5 & 0 \\-22 & 27 \end{bmatrix}\)
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Pertanyaan 2 dari 13
2. Pertanyaan
1 pointsPak Tarno seorang pengusaha roti yang menyetorkan dagangannya ke tiga toko roti di Jogjakarta. Tabel banyaknya roti yang disetorkan setiap harinya sebagai berikut:
Roti A Roti B Roti C Toko A 20 20 15 Toko B 15 15 20 Toko C 10 20 15 Harga sebungkus roti A, roti B, dan roti C berturut-turut adalah Rp3.000,00, Rp4.000,00, dan Rp5.000,00.
Pemasukan harian yang diterima Pak Tarno dari setiap toko A, toko B, dan toko C berturut-turut adalah…
Benar
\(\begin{bmatrix}20 & 20&15\\15&15&20\\10&20&15 \end{bmatrix}\cdot \begin{bmatrix}3000\\4000\\5000 \end{bmatrix}= \begin{bmatrix}20(3000) + 20(4000) + 15(5000)\\15(3000) + 15(4000) + 20(5000) \\10(3000) + 20(4000) + 15(5000)\end{bmatrix}\)
Jawaban: Rp215.000,00; Rp205.000,00; dan Rp185.000,00
Salah
\(\begin{bmatrix}20 & 20&15\\15&15&20\\10&20&15 \end{bmatrix}\cdot \begin{bmatrix}3000\\4000\\5000 \end{bmatrix}= \begin{bmatrix}20(3000) + 20(4000) + 15(5000)\\15(3000) + 15(4000) + 20(5000) \\10(3000) + 20(4000) + 15(5000)\end{bmatrix}\)
Jawaban: Rp215.000,00; Rp205.000,00; dan Rp185.000,00
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Pertanyaan 3 dari 13
3. Pertanyaan
1 pointsJika \(A = \begin{bmatrix}1 & 0 & -2 \\5 & -3 & 6 \end{bmatrix}\) dan \(B = \begin{bmatrix}0 & 1 & -7 \\5 & -3 & 2 \end{bmatrix}\), maka nilai dari \(A \cdot B^T = \dotso\)
Benar
\(A \cdot B^T = \begin{bmatrix}1 & 0 & -2 \\5 & -3 & 6 \end{bmatrix} \cdot \begin{bmatrix}0 & 5 \\1 & -3 \\-7&2 \end{bmatrix}\)
\(A \cdot B^T = \begin{bmatrix}14 & 1 \\-45 & 46 \end{bmatrix}\)
Salah
\(A \cdot B^T = \begin{bmatrix}1 & 0 & -2 \\5 & -3 & 6 \end{bmatrix} \cdot \begin{bmatrix}0 & 5 \\1 & -3 \\-7&2 \end{bmatrix}\)
\(A \cdot B^T = \begin{bmatrix}14 & 1 \\-45 & 46 \end{bmatrix}\)
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Pertanyaan 4 dari 13
4. Pertanyaan
1 pointsJika \(\begin{bmatrix}p + q & -2 \\p\:-\:q& 3 \end{bmatrix} = \begin{bmatrix}8 & -2 \\2& 3 \end{bmatrix}\), maka nilai dari \(2p \:-\:q\) adalah…
Benar
\(p + q = 8 \dotso \color{red} (1)\)
\(p \:-\: q = 2 \dotso \color{red} (2)\)
Eliminasi persamaan (1) dan (2), diperoleh \(p = 5\) dan \(q = 3\)
\(2p \:-\:q = 2(5)\:-\:3 = 7\)
Salah
\(p + q = 8 \dotso \color{red} (1)\)
\(p \:-\: q = 2 \dotso \color{red} (2)\)
Eliminasi persamaan (1) dan (2), diperoleh \(p = 5\) dan \(q = 3\)
\(2p \:-\:q = 2(5)\:-\:3 = 7\)
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Pertanyaan 5 dari 13
5. Pertanyaan
1 pointsJika \(\begin{bmatrix}-3 & 9\\-5&14\end{bmatrix} = \begin{bmatrix}3 & a\\a + 2b &-2\end{bmatrix}\cdot \begin{bmatrix}-1 & 4\\0 &3\end{bmatrix}\), maka nilai dari \(a \times b \) adalah…
Benar
\(\begin{bmatrix}-3 & 9\\-5&14\end{bmatrix} = \begin{bmatrix}-3 & 12 + 3a\\-a\:-\:2b &4a + 8b\:-\:6\end{bmatrix}\)
\(9 = 12 + 3a\)
\(-3 = 3a\)
\(a = -1\)
\(-5 = -a\:-\:2b\)
\(-5 = 1\:-\:2b\)
\(2b = 6\)
\(b = 3\)
\(a \times b = -3\)
Salah
\(\begin{bmatrix}-3 & 9\\-5&14\end{bmatrix} = \begin{bmatrix}-3 & 12 + 3a\\-a\:-\:2b &4a + 8b\:-\:6\end{bmatrix}\)
\(9 = 12 + 3a\)
\(-3 = 3a\)
\(a = -1\)
\(-5 = -a\:-\:2b\)
\(-5 = 1\:-\:2b\)
\(2b = 6\)
\(b = 3\)
\(a \times b = -3\)
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Pertanyaan 6 dari 13
6. Pertanyaan
1 points\(\begin{bmatrix}4 & 7\\-1& -2\end{bmatrix}\cdot \textbf{X} = \begin{bmatrix}3& -4\\5& 6\end{bmatrix}\), maka matriks X sama dengan…
Benar
\(\textbf{X} =\begin{bmatrix}4 & 7\\-1& -2\end{bmatrix}^{-1} \cdot \begin{bmatrix}3& -4\\5& 6\end{bmatrix}\)
\(\textbf{X} = \dfrac{1}{-8\:-\:(-7)}\begin{bmatrix}-2 & -7\\1& 4\end{bmatrix}\cdot \begin{bmatrix}3& -4\\5& 6\end{bmatrix}\)
\(\textbf{X} = (-1) \cdot \begin{bmatrix}-41&-34\\23& 20\end{bmatrix}\)
\(\textbf{X} = \begin{bmatrix}41&34\\-23& -20\end{bmatrix}\)
Salah
\(\textbf{X} =\begin{bmatrix}4 & 7\\-1& -2\end{bmatrix}^{-1} \cdot \begin{bmatrix}3& -4\\5& 6\end{bmatrix}\)
\(\textbf{X} = \dfrac{1}{-8\:-\:(-7)}\begin{bmatrix}-2 & -7\\1& 4\end{bmatrix}\cdot \begin{bmatrix}3& -4\\5& 6\end{bmatrix}\)
\(\textbf{X} = (-1) \cdot \begin{bmatrix}-41&-34\\23& 20\end{bmatrix}\)
\(\textbf{X} = \begin{bmatrix}41&34\\-23& -20\end{bmatrix}\)
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Pertanyaan 7 dari 13
7. Pertanyaan
1 pointsNilai \(x\) yang memenuhi determinan matriks \(\begin{bmatrix}x & x \\4 & x \end{bmatrix}\) sama dengan determinan matriks \(\begin{bmatrix}-2 & -3 \\2 & -3 \end{bmatrix}\) adalah…
Benar
\(x^2 \:-\:4x = 6\:-\:(-6)\)
\(x^2 \:-\:4x = 12\)
\(x^2\:-\:4x\:-\:12 = 0\)
\((x\:-\:6)(x + 2) = 0\)
\(x\:-\:6 = 0 \rightarrow x = 6\)
\(x + 2 = 0 \rightarrow x = -2\)
Salah
\(x^2 \:-\:4x = 6\:-\:(-6)\)
\(x^2 \:-\:4x = 12\)
\(x^2\:-\:4x\:-\:12 = 0\)
\((x\:-\:6)(x + 2) = 0\)
\(x\:-\:6 = 0 \rightarrow x = 6\)
\(x + 2 = 0 \rightarrow x = -2\)
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Pertanyaan 8 dari 13
8. Pertanyaan
1 pointsJika \(a\) adalah bilangan bulat, dan matriks \(\begin{bmatrix}2 & 1 & 2 \\a & 1 & a\\5& 6& 7 \end{bmatrix}\) tidak mempunyai invers, maka nilai \(a\) sama dengan…
Benar
Matriks yang tidak memiliki invers, maka determinannya sama dengan nol.
\(2\cdot \begin{bmatrix}1 & a\\6&7\end{bmatrix}\:-\:1\cdot \begin{bmatrix}a & a\\5&7\end{bmatrix} + 2\cdot \begin{bmatrix}a & 1\\5&6\end{bmatrix} = 0\)
\(2(7\:-\:6a)\:-\:1(7a\:-\:5a) + 2(6a\:-\:5) = 0\)
\(14\:-\:12a\:-\:7a + 5a + 12a \:-\:10 = 0\)
\(-2a + 4 = 0\)
\(a = 2\)
Salah
Matriks yang tidak memiliki invers, maka determinannya sama dengan nol.
\(2\cdot \begin{bmatrix}1 & a\\6&7\end{bmatrix}\:-\:1\cdot \begin{bmatrix}a & a\\5&7\end{bmatrix} + 2\cdot \begin{bmatrix}a & 1\\5&6\end{bmatrix} = 0\)
\(2(7\:-\:6a)\:-\:1(7a\:-\:5a) + 2(6a\:-\:5) = 0\)
\(14\:-\:12a\:-\:7a + 5a + 12a \:-\:10 = 0\)
\(-2a + 4 = 0\)
\(a = 2\)
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Pertanyaan 9 dari 13
9. Pertanyaan
1 pointsDitentukan sistem persamaan linear:
\(5x + 2y = 1\)
\(3x\:-\:6y = -2\)
Jika \(y = \dfrac{p}{\text{det }\begin{bmatrix}5 & 2 \\3 & -6 \end{bmatrix}}\), maka nilai \(p\) adalah…
Benar
\(\begin{bmatrix}5 & 2 \\3 & -6 \end{bmatrix}\cdot \begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}1\\-2\end{bmatrix}\)
dengan metode cramer,
\(x = \dfrac{\text{det} \begin{bmatrix}1 & 2 \\-2 & -6 \end{bmatrix}}{\text{det } \begin{bmatrix}5 & 2 \\3 & -6 \end{bmatrix}}\)
\(y = \dfrac{\text{det} \begin{bmatrix}5 & 1 \\3& -2 \end{bmatrix}}{\text{det } \begin{bmatrix}5 & 2 \\3 & -6 \end{bmatrix}}\)
\(p = \text{det}\begin{bmatrix}5 & 1 \\3& -2 \end{bmatrix}\)
\(p = 5(-2)\:-\:1(3) = -13\)
Salah
\(\begin{bmatrix}5 & 2 \\3 & -6 \end{bmatrix}\cdot \begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}1\\-2\end{bmatrix}\)
dengan metode cramer,
\(x = \dfrac{\text{det} \begin{bmatrix}1 & 2 \\-2 & -6 \end{bmatrix}}{\text{det } \begin{bmatrix}5 & 2 \\3 & -6 \end{bmatrix}}\)
\(y = \dfrac{\text{det} \begin{bmatrix}5 & 1 \\3& -2 \end{bmatrix}}{\text{det } \begin{bmatrix}5 & 2 \\3 & -6 \end{bmatrix}}\)
\(p = \text{det}\begin{bmatrix}5 & 1 \\3& -2 \end{bmatrix}\)
\(p = 5(-2)\:-\:1(3) = -13\)
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Pertanyaan 10 dari 13
10. Pertanyaan
1 pointsJika \(\text{A} = \begin{bmatrix}-3 & 4 \\2& -4 \end{bmatrix}\), maka determinan \(3\text{A}^2\) adalah…
Benar
Determinan matriks A = 12 − 8 = 4
Determinan 3 A² = 3² (det A)²
Determinan 3 A² = 9 (4)² = 144
Salah
Determinan matriks A = 12 − 8 = 4
Determinan 3 A² = 3² (det A)²
Determinan 3 A² = 9 (4)² = 144
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Pertanyaan 11 dari 13
11. Pertanyaan
1 pointsDiketahui matriks \(\text{A} = \begin{bmatrix}2 & 0&11 \\5&4&-3\\16&3&-5\end{bmatrix}\) dan \(\text{B} = \begin{bmatrix}-7 & 1&2 \\3&2&-4\\6&-7&5\end{bmatrix}\). Jika A − B = C, maka nilai dari determinan matriks C adalah…
Benar
\(\text{C} = \begin{bmatrix}9 &-1&9 \\2&2&1\\10&10&-10\end{bmatrix}\)
\(\text{Det C} = 9\cdot \text{det}\begin{bmatrix}2 &1\\10&-10\end{bmatrix} + 1 9\cdot \text{det}\begin{bmatrix}2 &1\\10&-10\end{bmatrix} + 99\cdot \text{det}\begin{bmatrix}2 &2\\10&10\end{bmatrix}\)
\(\text{Det C} = 9(-20\:-\:10) + 1(-20\:-\:10) + 9(20\:-\:20)\)
\(\text{Det C} = -270\:-\:30 = -300\)
Salah
\(\text{C} = \begin{bmatrix}9 &-1&9 \\2&2&1\\10&10&-10\end{bmatrix}\)
\(\text{Det C} = 9\cdot \text{det}\begin{bmatrix}2 &1\\10&-10\end{bmatrix} + 1 9\cdot \text{det}\begin{bmatrix}2 &1\\10&-10\end{bmatrix} + 99\cdot \text{det}\begin{bmatrix}2 &2\\10&10\end{bmatrix}\)
\(\text{Det C} = 9(-20\:-\:10) + 1(-20\:-\:10) + 9(20\:-\:20)\)
\(\text{Det C} = -270\:-\:30 = -300\)
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Pertanyaan 12 dari 13
12. Pertanyaan
1 pointsDiketahui matriks \(A=\begin{bmatrix}-2 & 3 \\-5& 7 \end{bmatrix}, \:B=\begin{bmatrix}4 &2 \\-6& -2 \end{bmatrix}\). Jika \(\text{C}\cdot \text{B}^{-1} = \text{A}\), maka matriks \(\text{C}^{\text{T}}\) adalah…
Benar
\(\text{C}\cdot \text{B}^{-1}\cdot \color{red} \text{B} \color{black} = \text{A}\cdot \color{red}\text{B}\)
\(\text{C} = \text{A}\cdot \text{B}\)
\(\text{C} = \begin{bmatrix}-2 & 3 \\-5& 7 \end{bmatrix}\cdot \begin{bmatrix}4 & 2 \\-6& -2 \end{bmatrix}\)
\(\text{C} = \begin{bmatrix}-26 & -10 \\-62 & -24 \end{bmatrix}\)
\(\text{C}^{\text{T}} = \begin{bmatrix}-26 & -62 \\-10 & -24 \end{bmatrix}\)
Salah
\(\text{C}\cdot \text{B}^{-1}\cdot \color{red} \text{B} \color{black} = \text{A}\cdot \color{red}\text{B}\)
\(\text{C} = \text{A}\cdot \text{B}\)
\(\text{C} = \begin{bmatrix}-2 & 3 \\-5& 7 \end{bmatrix}\cdot \begin{bmatrix}4 & 2 \\-6& -2 \end{bmatrix}\)
\(\text{C} = \begin{bmatrix}-26 & -10 \\-62 & -24 \end{bmatrix}\)
\(\text{C}^{\text{T}} = \begin{bmatrix}-26 & -62 \\-10 & -24 \end{bmatrix}\)
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Pertanyaan 13 dari 13
13. Pertanyaan
1 pointsDiketahui \(\begin{bmatrix}4 & -2 \\5 & -4 \end{bmatrix} \cdot \text{B} \cdot \begin{bmatrix}-2 & 3 \\1& -3 \end{bmatrix}\cdot \begin{bmatrix}2 & 2 \\3 &4 \end{bmatrix} = \begin{bmatrix}4 &2 \\2 & 10 \end{bmatrix}\cdot \begin{bmatrix}-2 & 3 \\-1 & 3\end{bmatrix}\), nilai dari determinan matriks B adalah…
Benar
Gunakan sifat determinan matriks berikut:
Determinan (A. B. C) = det A. det B. det C
(−6). det B. (3). (2) = (36). (−3)
(−36). det B = 36 . (−3)
det B = 3
Salah
Gunakan sifat determinan matriks berikut:
Determinan (A. B. C) = det A. det B. det C
(−6). det B. (3). (2) = (36). (−3)
(−36). det B = 36 . (−3)
det B = 3