Chapter 11: Q. 8 (page 755)

If AX = B represents a matrix equation where A is a
nonsingular matrix, then we can solve the equation using
X = ________.

Short Answer

Expert verified

$A^{- 1} B$ .

Step by step solution

Step 1. Given Information

A non singular matrix.

Step 2. Calculation

$C o n s i d e r, [\begin{matrix} 2 & - 3 \\ 1 & 1 \end{matrix}] [\begin{matrix} x \\ y \end{matrix}] = [\begin{matrix} 12 \\ 1 \end{matrix}] f i n d A^{- 1} [\begin{matrix} 2 & - 3 \\ 1 & 1 \end{matrix}] [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] R_{1} \leftrightarrow R_{2} [\begin{matrix} 1 & 1 \\ 2 & - 3 \end{matrix}] [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}] R_{2} \to R_{2} - 2 R_{1} [\begin{matrix} 1 & 1 \\ 0 & - 5 \end{matrix}] [\begin{matrix} 0 & 1 \\ 1 & - 2 \end{matrix}] R_{2} \to - \frac{1}{5} R_{2} [\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix}] [\begin{matrix} 0 & 1 \\ - \frac{1}{5} & \frac{2}{5} \end{matrix}] R_{1} \to R_{1} - R_{2} [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] [\begin{matrix} \frac{1}{5} & \frac{3}{5} \\ - \frac{1}{5} & \frac{2}{5} \end{matrix}]$

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If AX = B represents a matrix equation where A is a
nonsingular matrix, then we can solve the equation using
X = ________.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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If AX = B represents a matrix equation where A is anonsingular matrix, then we can solve the equation usingX = ________.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

If AX = B represents a matrix equation where A is a
nonsingular matrix, then we can solve the equation using
X = ________.