Matrix Calculator
Kuwonjezera, kugawa, kusinthira, ndi kupeza determinant ndi inverted ya masentimita pa intaneti.
Zachidule
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.
Mafunso ofunsidwa nthawi zambiri
Kodi kukula masentimita ndi othandiza?
Mukhoza kuika mnda ndi masamba kuchokera 1 × 1 mpaka 5 × 5 kwa mzere uliwonse. Determinant ndi inverted ayenera square mzere.
N’chifukwa chiyani sindingathe kuwonjezereka anga awiri masentimita?
Matrix kuwonjezereka amafuna idadi ya mafelemu a mafelemu achiwiri kuti azikhala ndi idadi ya mafelemu achiwiri. The calculator ikuuzani pamene zigawo sizikugwirizana.
Kodi machitidwe a machitidwe ali ndi machitidwe osiyanasiyana?
A square matiritsi alibe inverted pamene determinant yake ndi zero - amatchedwa sing'anga. The calculator akudziwitsa izi m'malo mwa zotsatira.
Kodi ndingapeze chosankha cha 2 × 2 kapena 3 × 3 masentimita?
Ikani matiriji ku square, gwiritsani ntchito ziwerengero ndi kusankha ntchito yosankhira. Kwa 2×2 imawerengera ad − bc; kwa 3×3 imawonjezeka m'gulu. Chida cha zero chimatanthauza kuti matiriji ndi amodzi ndipo samakhala ndi kusinthika.
Kodi ndi chiyani kusinthidwa kwa mafoni?
The transpose swaps mzere ndi masamba, kotero kulowa mzere i, mzere j amapita mzere j, mzere i. A 2 × 3 masentimita adzakhala 3 × 2. Sankhani transpose ntchito kuona izo kwa kukula iliyonse.
Kodi ndi mmene scalar kugawa ntchito?
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.
Kodi machitidwe osiyanasiyana a matrix ndi osiyana?
No. In general A×B is not the same as B×A, and one order may be valid while the other is not defined at all, because multiplication depends on the columns of the first matrix matching the rows of the second.
Zimenezi ndi zowerengera zokhudzana ndi malangizo amtundu uliwonse, si zokhudzana ndi ndalama, zamoyo kapena zokhudzana ndi ndalama.