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  1. Glossary
  2. /Mathematics
  3. /Matrix

What is Matrix?

In short

A matrix is a rectangular arrangement of numbers in rows and columns, written inside brackets. A matrix with mmm rows and nnn columns is an m×nm \times nm×n matrix.

In simple words

Two matrices of the same size can be added by adding matching entries. To multiply AAA by BBB, the number of columns of AAA must equal the number of rows of BBB. Matrix multiplication is not commutative: usually AB≠BAAB \neq BAAB=BA. The identity matrix III leaves any matrix unchanged. The determinant of a 2×22 \times 22×2 matrix with rows (a,b)(a, b)(a,b) and (c,d)(c, d)(c,d) is ad−bcad - bcad−bc, and the matrix has an inverse only if this is not zero.

Example

The matrix with rows (1,2)(1, 2)(1,2) and (3,4)(3, 4)(3,4) has determinant 1×4−2×3=−21 \times 4 - 2 \times 3 = -21×4−2×3=−2, so it has an inverse. Its transpose has rows (1,3)(1, 3)(1,3) and (2,4)(2, 4)(2,4).

Also searched as: a.t[0,1].

Learn it properly

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Related terms

  • Vector
  • Linear Equation

← All glossary terms

Learn it in

  1. Matrices and Matrix AlgebraClass 11 to 12
  2. DeterminantsClass 11 to 12
  3. Inverse of a Matrix and Systems of Linear EquationsClass 11 to 12
All lessons on this topic →

Practise

  1. Three roads join the junctions P, Q and R in a triangle…Hard
  2. Use row operations on [A | I] to find the inverse of A = 1, 1, 0; 1, 2, 1; 0, 1, 2…
Medium
  • The system x + 2y + z = 0, 2x + ky + 3z = 0 and x + y + 2z = 0 has solutions other than…Hard
  • Consider x + y + z = 6, x + 2y + 3z = 10 and x + 2y + λ z = µ…Hard
    • All problems on this topic →

    Quick questions

    1. Row operations turn the augmented matrix of a system in three unknowns into one whose…Hard
    2. For which value of c does the system x + y = 1, 2x + 2y = c have a solution?Hard
    3. A homogeneous system AX = O in three unknowns has a solution other than X = O. What must…Medium

    More Mathematics terms

    1. Algebraic Identity
    2. Arithmetic Progression
    3. Complex Number
    4. Derivative
    5. Function
    6. Isosceles Triangle
    All Mathematics terms →

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