大学线性代数英文题目Compute the determinant and state whether the matr
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大学线性代数英文题目
Compute the determinant and state whether the matrix is singular or nonsingular.
A=1 1 1 1
2 -1 3 2
0 1 2 1
0 0 7 3
我忘记怎么把4X4矩阵化成3X3了,求公式.
书上写计算行列式det(A)(A是3X3矩阵)写了两种算法,一种是:det(A)=a11A11+a12A12+a13A13(数字都是下标)然后where A1j=(-1)^(1+j)det(M1j) j=1,2,3.
另一种是det(A)=a11a22a33-a11a32a23-a12a21a33+a12a31a23+a13a21a32-a13a31a22
我想问这两种算法是相等的吗?然后我看不懂A11是什么意思,是要把矩阵怎么转换呢?
Compute the determinant and state whether the matrix is singular or nonsingular.
A=1 1 1 1
2 -1 3 2
0 1 2 1
0 0 7 3
我忘记怎么把4X4矩阵化成3X3了,求公式.
书上写计算行列式det(A)(A是3X3矩阵)写了两种算法,一种是:det(A)=a11A11+a12A12+a13A13(数字都是下标)然后where A1j=(-1)^(1+j)det(M1j) j=1,2,3.
另一种是det(A)=a11a22a33-a11a32a23-a12a21a33+a12a31a23+a13a21a32-a13a31a22
我想问这两种算法是相等的吗?然后我看不懂A11是什么意思,是要把矩阵怎么转换呢?
1 1 1 1 1 1 1 1 1 1 1 1
|A|= 2 -1 3 2 = 0 -3 1 0 = (-1) 0 1 2 1 =0 (两行成比例)
0 1 2 1 0 1 2 1 0 0 7 3
0 0 7 3 0 0 7 3 0 0 7 3
所以矩阵A是奇异的 或 不可逆
det(A)=a11A11+a12A12+a13A13 这个是降阶算法
det(A)=a11a22a33-a11a32a23-a12a21a33+a12a31a23+a13a21a32-a13a31a22 这是对角线法
A11是与元素a11对应的代数余子式
|A|= 2 -1 3 2 = 0 -3 1 0 = (-1) 0 1 2 1 =0 (两行成比例)
0 1 2 1 0 1 2 1 0 0 7 3
0 0 7 3 0 0 7 3 0 0 7 3
所以矩阵A是奇异的 或 不可逆
det(A)=a11A11+a12A12+a13A13 这个是降阶算法
det(A)=a11a22a33-a11a32a23-a12a21a33+a12a31a23+a13a21a32-a13a31a22 这是对角线法
A11是与元素a11对应的代数余子式
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