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Aljabar Linear Contoh
[171290181][4.50.5-4.5-1013.5-0.5-2.5]
Langkah 1
Langkah 1.1
Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is 3×3 and the second matrix is 3×3.
Langkah 1.2
Kalikan setiap baris pada matriks pertama dengan setiap kolom pada matriks kedua.
[1⋅4.5+7⋅-1+1⋅3.51⋅0.5+7⋅0+1⋅-0.51⋅-4.5+7⋅1+1⋅-2.52⋅4.5+9⋅-1+0⋅3.52⋅0.5+9⋅0+0⋅-0.52⋅-4.5+9⋅1+0⋅-2.51⋅4.5+8⋅-1+1⋅3.51⋅0.5+8⋅0+1⋅-0.51⋅-4.5+8⋅1+1⋅-2.5]
Langkah 1.3
Sederhanakan setiap elemen dalam matriks dengan mengalikan semua pernyataannya.
[100010001]
[100010001]
Langkah 2
Langkah 2.1
Choose the row or column with the most 0 elements. If there are no 0 elements choose any row or column. Multiply every element in row 1 by its cofactor and add.
Langkah 2.1.1
Consider the corresponding sign chart.
|+-+-+-+-+|
Langkah 2.1.2
The cofactor is the minor with the sign changed if the indices match a - position on the sign chart.
Langkah 2.1.3
The minor for a11 is the determinant with row 1 and column 1 deleted.
|1001|
Langkah 2.1.4
Multiply element a11 by its cofactor.
1|1001|
Langkah 2.1.5
The minor for a12 is the determinant with row 1 and column 2 deleted.
|0001|
Langkah 2.1.6
Multiply element a12 by its cofactor.
0|0001|
Langkah 2.1.7
The minor for a13 is the determinant with row 1 and column 3 deleted.
|0100|
Langkah 2.1.8
Multiply element a13 by its cofactor.
0|0100|
Langkah 2.1.9
Add the terms together.
1|1001|+0|0001|+0|0100|
1|1001|+0|0001|+0|0100|
Langkah 2.2
Kalikan 0 dengan |0001|.
1|1001|+0+0|0100|
Langkah 2.3
Kalikan 0 dengan |0100|.
1|1001|+0+0
Langkah 2.4
Evaluasi |1001|.
Langkah 2.4.1
Determinan dari matriks 2×2 dapat dicari menggunakan rumus |abcd|=ad-cb.
1(1⋅1+0⋅0)+0+0
Langkah 2.4.2
Sederhanakan determinannya.
Langkah 2.4.2.1
Sederhanakan setiap suku.
Langkah 2.4.2.1.1
Kalikan 1 dengan 1.
1(1+0⋅0)+0+0
Langkah 2.4.2.1.2
Kalikan 0 dengan 0.
1(1+0)+0+0
1(1+0)+0+0
Langkah 2.4.2.2
Tambahkan 1 dan 0.
1⋅1+0+0
1⋅1+0+0
1⋅1+0+0
Langkah 2.5
Sederhanakan determinannya.
Langkah 2.5.1
Kalikan 1 dengan 1.
1+0+0
Langkah 2.5.2
Tambahkan 1 dan 0.
1+0
Langkah 2.5.3
Tambahkan 1 dan 0.
1
1
1
Langkah 3
Since the determinant is non-zero, the inverse exists.
Langkah 4
Set up a 3×6 matrix where the left half is the original matrix and the right half is its identity matrix.
[100100010010001001]
Langkah 5
The right half of the reduced row echelon form is the inverse.
[100010001]