Ngā Tauira Pātai e Matapaki ana i te Āhua ōrite o ngā Matrices e Rua
He pūtaiao taketake te pāngarau, ā, he maha ngā peka hohonu, ko tētahi o ēnei ko te arorangi rārangi, ā, he mea nui tonu te kōrero mō ngā matihiko. I roto i te horopaki o te arorangi rārangi, he kaupapa nui te ariā o te ōritetanga o ngā matihiko (te ōritetanga rānei) ā, e whakamahia ana i roto i ngā tono pāngarau me te hangarau. Ka matapakihia e tēnei tuhinga te ōritetanga o ngā matihiko e rua, me pēhea te whakatairite i ēnei ōritetanga, ā, ka whakaratohia he tauira raruraru me ā rātou otinga hei āwhina i te mārama.
Te Mārama ki te Āhua ōrite o ngā Matrix e Rua
E kiia ana he ōrite ngā matihiko e rua mēnā he ōrite te rahi, ā, he ōrite hoki ngā huānga katoa e rite ana i roto i ngā matihiko. I roto i te pāngarau, e kiia ana he ōrite ngā matihiko e rua \(A\) me \(B\), ka tuhia \(A = B\), mēnā, ā, mēnā anake:
1. He ōrite te maha o ngā rarangi me ngā pou o ngā matihiko e rua.
2. He ōrite ia huānga kei te tūranga ōrite i roto i ngā matihiko e rua.
Me kī ko \(A = [a_{ij}]\) me \(B = [b_{ij}]\), kātahi ko \(A = B\) mēnā, ā, mēnā anake:
– He rite te rahi o \(A\) me \(B\) (hei tauira, ngā matihiko \(m \times n\)).
– \(a_{ij} = b_{ij}\) mō ia huānga (i, j) i roto i te matihiko.
Ngā Hipanga hei Whakatau i te Āhuatanga Rite o te Matrix
1. Tirohia te Rahi o te Matrix: Kia rite te maha o ngā rarangi me ngā pou o ngā matrices. Ki te kore e rite te rahi, kāore e taea te whakarite anō.
2. Whakatauritea ia Huānga: Tirohia ngā huānga e rite ana i roto i ngā matihiko e rua. Mena he huānga kāore i te ōrite, kāore ngā matihiko i te ōrite.
Ngā Pātai Tauira me te Kōrero
Me titiro tātou ki ētahi tauira rapanga e pā ana ki te ōritetanga o ngā matihiko e rua me ā rāua otinga hei whakamārama i tēnei ariā.
Tauira Pātai 1
Hoatu ngā matihiko e rua e whai ake nei, ā, whakatauhia mēnā he ōrite, kāore rānei:
\[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \]
\[ B = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \]
Kōrero:
– Hipanga 1: Tirohia te rahi o te matihiko.
He rite te rahi o ngā matihiko \(A\) me \(B\) \(2 \times 3\). He rite tonu te maha o ngā rarangi me ngā pou o ngā matihiko e rua.
– Hipanga 2: Whakatauritea ia huānga e rite ana.
Whakatauritea ngā huānga \(a_{ij}\) me \(b_{ij}\):
– \(a_{11} = 1\) me \(b_{11} = 1\)
– \(a_{12} = 2\) me \(b_{12} = 2\)
– \(a_{13} = 3\) me \(b_{13} = 3\)
– \(a_{21} = 4\) me \(b_{21} = 4\)
– \(a_{22} = 5\) me \(b_{22} = 5\)
– \(a_{23} = 6\) me \(b_{23} = 6\)
He rite tonu ngā huānga katoa e pā ana.
Nō reira, he ōrite ngā matihiko \(A\) me \(B\).
Tauira Pātai 2
E ai ki ngā matihiko e rua e whai ake nei, he ōrite rāua?
\[ C = \begin{bmatrix} 1 me te 2 \\ 3 me te 4 \end{bmatrix} \]
\[ D = \begin{bmatrix} 1 me te 2 \\ 3 me te 5 \end{bmatrix} \]
Kōrero:
– Hipanga 1: Tirohia te rahi o te matihiko.
He rite te rahi o ngā matihiko \(C\) me \(D\) \(2 \times 2\). He rite tonu te maha o ngā rarangi me ngā pou o ngā matihiko e rua.
– Hipanga 2: Whakatauritea ia huānga e rite ana.
Whakatauritea ngā huānga \(c_{ij}\) me \(d_{ij}\):
– \(c_{11} = 1\) me \(d_{11} = 1\)
– \(c_{12} = 2\) me \(d_{12} = 2\)
– \(c_{21} = 3\) me \(d_{21} = 3\)
– \(c_{22} = 4\) me \(d_{22} = 5\)
I konei, he motuhake ngā huānga \(c_{22}\) me \(d_{22}\) (4 ≠ 5).
Nō reira, kāore ngā matihiko \(C\) me \(D\) i te ōrite.
Tauira Pātai 3
E rua ngā matihiko e whai ake nei:
\[ E = \begin{bmatrix} 7 me te 8 \end{bmatrix} \]
\[ F = \begin{bmatrix} 7 me te 8 \\ 9 me te 10 \end{bmatrix} \]
He ōrite ēnei matihiko e rua?
Kōrero:
– Hipanga 1: Tirohia te rahi o te matihiko.
He rahi te matihiko \(E\) \(1 \times 2\) ko te rahi ia o \(F\) \(2 \times 2\). Kāore ngā rahi o ngā matihiko i te ōrite.
Nō reira, kāore ngā matihiko \(E\) me \(F\) i te ōrite nā te mea he rerekē ō rāua rahi.
Tauira Pātai 4
Me kī kei reira ngā matihiko e rua e whai ake nei:
\[ G = \begin{bmatrix} a me b \\ c me d \end{bmatrix} \]
\[ H = \begin{bmatrix} 1 me te 2 \\ 3 me te 4 \end{bmatrix} \]
Whakatauhia ngā uara o \(a, b, c, d\) kia ōrite ai a \(G\) me \(H\).
Kōrero:
E ai ki te whakamāramatanga o te ōritetanga, me ōrite ngā huānga e rite ana o \(G\) me \(H\):
– \(a = 1\)
– \(b = 2\)
– \(c = 3\)
– \(d = 4\)
Nō reira, mō \(G = H\), me whai uara \(1, 2, 3,\) me \(4\) ngā \(a, b, c, d\).
Whakamutunga
Mai i te matapakinga o ngā tauira pātai i runga ake nei, ka taea e tātou te whakatau i te tukanga mō te whakatau i te ōritetanga o ngā matihiko e rua:
1. Tirohia mēnā he ōrite te rahi o ngā matihiko e rua.
2. Whakatauritea ia huānga e rite ana, takitahi. Mena he ōrite ngā huānga katoa, he ōrite ngā matihiko e rua.
He mea nui te mārama ki te ōritetanga o ngā matihiko e rua ki te ako i te arapūrangi rārangi me ōna whakamahinga i roto i ngā momo marautanga. Mā te ōritetanga o ngā matihiko e rua ka taea e tātou te mahi i ētahi atu mahi pēnei i te tāpiri, te tango, me te whakarea me te ngāwari me te tika. Nō reira, he mea nui te mōhio ki tēnei ariā mō te ako pāngarau tonu.
