矩阵计算器
添加、乘法、转换和找到矩阵的决定因素和反向。
关于此计算器
A matrix calculator performs the core operations of linear algebra: addition and subtraction, multiplication, scalar multiplication, transpose, determinant and inverse for square matrices. Set the size, type in the numbers, and pick an operation to see the result matrix instantly.
You choose the number of rows and columns (up to 5×5), fill in the entries, and pick an operation. Addition and subtraction work entry by entry on two matrices of the same size; multiplication takes the dot product of each row of the first matrix with each column of the second, so the first matrix’s column count must equal the second’s row count. Transpose flips rows and columns, while the determinant and inverse apply only to square matrices — and the inverse exists only when the determinant is not zero.
For a worked example, the 2×2 matrix [[1, 2], [3, 4]] has determinant 1·4 − 2·3 = -2, and because that is non-zero it has an inverse, (1/-2)·[[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]]. Its transpose is [[1, 3], [2, 4]]. Students and engineers use it for solving linear systems, transforming coordinates and vectors, computer graphics, and checking linear-algebra homework quickly.
经常问到的问题
支持的大小矩阵大小是什么?
您可以为每个矩阵设置从 1 x1 至 5 x5 的行和列。 确定性和反向需要平方矩阵。
为何我不能将我的两个矩阵乘以数?
矩阵乘法要求第一个矩阵的列数等于第二个矩阵的行数。计算器在大小不匹配时会告诉你。
矩阵什么时候没有反向反应?
平方矩阵在决定数为零时没有反向反应,它被称为单数,计算器报告的是这个而不是结果。
如何找到 2x2 或 3x3 矩阵的决定因素?
设置矩阵为平方, 输入数字并选择决定因素操作。 对于 2x2, 它计算 ad- bc; 对于 3x3 则沿着一行展开。 零结果表示矩阵是单数, 没有反数 。
矩阵的转换是什么?
转换换行和列, 因此, i 行的条目, j列 j 移动到 j 行, i 列 A 2x3 矩阵变成 3x2 。 选择切换操作来查看任何大小 。
计算乘法如何起作用?
Every entry of the matrix is multiplied by the same number, so multiplying [[1, 2], [3, 4]] by 3 gives [[3, 6], [9, 12]]. It scales the whole matrix without changing its shape.
矩阵乘法混合性吗?
否。一般而言, AxB 与 BxA 不同,一个命令可能有效,而另一个命令则完全没有定义,因为乘法取决于第一个矩阵中与第二个矩阵行对应的列。
成果仅是一般指导的估计数,而不是财务、医疗或税务咨询。