4.7E: Mazoezi

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Mazoezi hufanya kamili

Tathmini ya Uamuzi wa Matrix 2 × 2

Katika mazoezi yafuatayo, tathmini uamuzi wa kila tumbo la mraba.

$\left[\begin{matrix}6&−2\\3&−1\end{matrix}\right]$

$\left[\begin{matrix}−4&8\\−3&5\end{matrix}\right]$

Jibu: $4$

$\left[\begin{matrix}−3&5\\0&−4\end{matrix}\right]$

$\left[\begin{matrix}−2&0\\7&−5\end{matrix}\right]$

Jibu: $10$

Tathmini ya Uamuzi wa Matrix 3 × 3

Katika mazoezi yafuatayo, tafuta na kisha tathmini watoto walioonyeshwa.

$\left|\begin{matrix}3&−1&4\\−1&0&−2\\−4&1&5\end{matrix}\right|$

Pata mdogo ⓐ$a_1$ ⓑ$b_2$ ⓒ$c_3$

$\left|\begin{matrix}−1&−3&2\\4&−2&−1\\−2&0&−3\end{matrix}\right|$

Pata mdogo ⓐ$a_1$ ⓑ$b_1$ ⓒ$c_2$

Jibu: ⓐ 6 ⓑ$−14$ ⓒ$−6$

$\left|\begin{matrix}2&−3&−4\\−1&2&−3\\0&−1&−2\end{matrix}\right|$

Pata mdogo ⓐ$a_2$ ⓑ$b_2$ ⓒ$c_2$

$\left|\begin{matrix}−2&−2&3\\1&−3&0\\−2&3&−2\end{matrix}\right|$

Pata mdogo ⓐ$a_3$ ⓑ$b_3$ ⓒ$c_3$

Jibu: ⓐ 9 ⓑ$−3$ ⓒ 8

Katika mazoezi yafuatayo, tathmini kila uamuzi kwa kupanua na watoto kando ya mstari wa kwanza.

$\left|\begin{matrix}−2&3&−1\\−1&2&−2\\3&1&−3\end{matrix}\right|$

$\left|\begin{matrix}4&−1&−2\\−3&−2&1\\−2&−5&7\end{matrix}\right|$

Jibu: $−77$

$\left|\begin{matrix}−2&−3&−4\\5&−6&7\\−1&2&0\end{matrix}\right|$

$\left|\begin{matrix}1&3&−2\\5&−6&4\\0&−2&−1\end{matrix}\right|$

Jibu: $49$

Katika mazoezi yafuatayo, tathmini kila uamuzi kwa kupanua na watoto.

$\left|\begin{matrix}−5&−1&−4\\4&0&−3\\2&−2&6\end{matrix}\right|$

$\left|\begin{matrix}4&−1&3\\3&−2&2\\−1&0&4\end{matrix}\right|$

Jibu: $−24$

$\left|\begin{matrix}3&5&4\\−1&3&0\\−2&6&1\end{matrix}\right|$

$\left|\begin{matrix}2&−4&−3\\5&−1&−4\\3&2&0\end{matrix}\right|$

Jibu: $25$

Tumia Utawala wa Cramer wa Kutatua Mifumo ya Equations

Katika mazoezi yafuatayo, tatua kila mfumo wa equations kwa kutumia Kanuni ya Cramer.

$\left\{\begin{array} {l} −2x+3y=3\\x+3y=12\end{array}\right.$

$\left\{\begin{array} {l} x−2y=−5\\2x−3y=−4\end{array}\right.$

Jibu: $(7,6)$

$\left\{\begin{array} {l} x−3y=−9\\2x+5y=4\end{array}\right.$

$\left\{\begin{array} {l} 2x+y=−4\\3x−2y=−6\end{array}\right.$

Jibu: $(−2,0)$

$\left\{\begin{array} {l} x−2y=−5\\2x−3y=−4\end{array}\right.$

$\left\{\begin{array} {l} x−3y=−9\\2x+5y=4\end{array}\right.$

Jibu: $(−3,2)$

$\left\{\begin{array} {l} 5x−3y=−1\\2x−y=2\end{array}\right.$

$\left\{\begin{array} {l} 3x+8y=−3\\2x+5y=−3\end{array}\right.$

Jibu: $(−9,3)$

$\left\{\begin{array} {l} 6x−5y+2z=3\\2x+y−4z=5\\3x−3y+z=−1 \end{array}\right.$

$\left\{\begin{array} {l} 4x−3y+z=7\\2x−5y−4z=3\\3x−2y−2z=−7\end{array}\right.$

Jibu: $(−3,−5,4)$

$\left\{\begin{array} {l} 2x−5y+3z=8\\3x−y+4z=7\\x+3y+2z=−3\end{array}\right.$

$\left\{\begin{array} {l} 11x+9y+2z=−9\\7x+5y+3z=−7\\4x+3y+z=−3\end{array}\right.$

Jibu: $(2,−3,−2)$

$\left\{\begin{array} {l} x+2z=0\\4y+3z=−2\\2x−5y=3\end{array}\right.$

$\left\{\begin{array} {l} 2x+5y=4\\3y−z=3\\4x+3z=−3\end{array}\right.$

Jibu: $(−3,2,3)$

$\left\{\begin{array} {l} 2y+3z=−1\\5x+3y=−6\\7x+z=1\end{array}\right.$

$\left\{\begin{array} {l} 3x−z=−3\\5y+2z=−6\\4x+3y=−8\end{array}\right.$

Jibu: $(−2,0,−3)$

$\left\{\begin{array} {l} 2x+y=3\\6x+3y=9\end{array}\right.$

$\left\{\begin{array} {l} x−4y=−1\\−3x+12y=3\end{array}\right.$

Jibu: ufumbuzi mkubwa sana

$\left\{\begin{array} {l} −3x−y=4\\6x+2y=−16\end{array}\right.$

$\left\{\begin{array} {l} 4x+3y=2\\20x+15y=5\end{array}\right.$

Jibu: isiyowiana

$\left\{\begin{array} {l} x+y−3z=−1\\y−z=0\\−x+2y=1\end{array}\right.$

$\left\{\begin{array} {l} 2x+3y+z=1\\2x+y+z=9\\3x+4y+2z=20\end{array}\right.$

Jibu: isiyowiana

$\left\{\begin{array} {l} 3x+4y−3z=−2\\2x+3y−z=−1\\2x+y−2z=6\end{array}\right.$

$\left\{\begin{array} {l} x−2y+3z=1\\x+y−3z=7\\3x−4y+5z=7\end{array}\right.$

Jibu: ufumbuzi mkubwa sana

Kutatua Maombi Kutumia Maamuzi

Katika mazoezi yafuatayo, onyesha kama pointi zilizopewa ni collinear.

$(0,1)$,$(2,0)$, na$(−2,2)$.

$(0,−5)$,$(−2,−2)$, na$(2,−8)$.

Jibu: ndiyo

$(4,−3)$,$(6,−4)$, na$(2,−2)$.

$(−2,1)$,$(−4,4)$, na$(0,−2)$.

Jibu: hapana

Mazoezi ya kuandika

Eleza tofauti kati ya tumbo la mraba na uamuzi wake. Kutoa mfano wa kila mmoja.

Eleza nini maana ya mdogo wa kuingia kwenye tumbo la mraba.

Jibu: Majibu yatatofautiana.

Eleza jinsi ya kuamua mstari au safu utakayotumia kupanua$3×3$ uamuzi.

Eleza hatua za kutatua mfumo wa equations kwa kutumia utawala wa Cramer.

Jibu: Majibu yatatofautiana.

Self Check

ⓐ Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

$Jedwali hili lina nguzo 4, safu 4 na mstari wa kichwa. Mstari wa kichwa huandika kila safu: I ca, kwa ujasiri, kwa msaada na hapana, siipati. safu ya kwanza ina kauli zifuatazo: Tathmini Determinant ya 2 na 2 Matrix, Tathmini Determinant ya 3 na 3 Matrix, Matumizi Cramer ya Utawala wa kutatua Systems of Equations, Kutatua Maombi Kutumia Maamuzi. Nguzo zilizobaki ni tupu.$

ⓑ Baada ya kuchunguza orodha hii, utafanya nini ili uwe na ujasiri kwa malengo yote?