Question
Download Solution PDFDetermine the transpose of a 3 × 3 matrix defined as A = [aij], for the aij = 2i - j
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Transpose of a Matrix:
The new matrix obtained by interchanging the rows and columns of the original matrix is called as the transpose of the matrix.
It is denoted by
For example:
Calculation:
Let matrix A =
a11 = 2 × (1) - 1 = 1
a12 = 2 × (1) - 2 = 0
a13 = 2 × (1) - 3 = -1
a21 = 2 × (2) - 1 = 3
a22 = 2 × (2) - 2 = 2
a23 = 2 × (2) - 3 = 1
a31 = 2 × (3) - 1 = 5
a32 = 2 × (3) - 2 = 4
a33 = 2 × (3) - 3 = 3
∴ A =
AT =
⇒ AT =
Additional Information
Properties of Transpose of a Matrix:
- The transpose of a matrix is the matrix itself:
- The transposes of equal matrices are also similar:
- The transpose of the sum/difference of two matrices is equivalent to the sum/difference of their transposes:
- The transpose of the product of two matrices is equivalent to the product of their transposes in reversed order:
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