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FM Scalar Multiplication

1.3 The Inverse of a Matrix

The Determinant of a 2×2 Matrix

  • The determinant of a 2 x 2 matrix can be calculated as:

\text { det }=A_{1,1} A_{2,2}-A_{1,2} A_{2,1}

  • The determinant of an identity matrix is equal to 1.

Example

A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right]

The determinant of the above matrix is:

\operatorname{det}=1 * 4-2 * 3=-2

Requirements for a Matrix to be Invertible

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1.2 Elementary Matrix Operations

Addition and Subtraction

  • Matrix addition and subtraction is carried out on an element-by-element basis. The element C_{i,j} in the resultant matrix is found by carrying out addition or subtraction with the corresponding elements; A_{i,j} and B_{i,j} in the other matrices.
  • Matrices can only be added or subtracted from one another if they have the same dimensions.

Examples

\left[\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right]+\left[\begin{array}{ll} 1 & 0 \\ 1 & 0 \end{array}\right]=\left[\begin{array}{ll} 2 & 2 \\ 1 & 1 \end{array}\right]

\left[\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right]-\left[\begin{array}{ll} 1 & 0 \\ 1 & 0 \end{array}\right]=\left[\begin{array}{cc} 0 & 2 \\ -1 & 1 \end{array}\right]

Scalar Multiplication

Read More »1.2 Elementary Matrix Operations