Chapter 4: Q2. (page 198)

Explain how to find the inverse of a $2 \times 2$ matrix.

Short Answer

Expert verified

The inverse of $2 \times 2$ matrix $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ is given by $A^{- 1} = \frac{1}{ad - bc} [\begin{matrix} d & - b \\ - c & a \end{matrix}]$ and $ad - bc \neq 0$ .

Step by step solution

- Description of step.

A $2 \times 2$ matrix means the matrix is having two rows and two columns.

- Definition of inverse of matrix.

A square matrixB is said to be an inverse of the square matrixA if $AB = BA = I$ where I is an identity matrix of the same order as that of matrix Aor B.

- Description of step.

The inverse of $2 \times 2$ matrix $A = [\begin{matrix} a & b \\ c & d \end{matrix}]$ is given by $A^{- 1} = \frac{1}{a d - b c} [\begin{matrix} d & - b \\ - c & a \end{matrix}]$ and $a d - b c \neq 0$ .

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Explain how to find the inverse of a $2 \times 2$ matrix.

Short Answer

Step by step solution

- Description of step.

- Definition of inverse of matrix.

- Description of step.

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Explain how to find the inverse of a2×2 matrix.

Short Answer

Step by step solution

­- Description of step.

­- Definition of inverse of matrix.

­- Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Decision Maths

Geometry

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Explain how to find the inverse of a $2 \times 2$ matrix.

- Description of step.

- Definition of inverse of matrix.

- Description of step.