Short Answer

TRUE OR FALSE?
There exists a matrix A such that $A (\begin{matrix} \begin{matrix} 1 & 2 \\ 1 & 2 \end{matrix} \end{matrix}) = (\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix})$ .

The statement is false.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Compute the matrix

The matrix is said to be invertible, if and only if the reduced row echelon form of the matrix has nonzero diagonal elements and for second order matrix, the determinant of the matrix should be nonzero.

Step 2: Apply the application of inverse

Consider the condition.

$A (\begin{matrix} \begin{matrix} 1 & 2 \\ 1 & 2 \end{matrix} \end{matrix}) = (\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}) \Rightarrow A = (\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}) {(\begin{matrix} \begin{matrix} 1 & 2 \\ 1 & 2 \end{matrix} \end{matrix})}^{- 1}$

If the determinant of the matrix is zero, then, this inverse does not exist.

As $d e t (\begin{matrix} 1 & 2 \\ 1 & 2 \end{matrix}) = 0$ thus, the inverse does not exist.

Therefore, the matrix does not exist.

The statement is false.

Find Study Materials for

Create Study Materials

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

TRUE OR FALSE?
There exists a matrix A such that $A (\begin{matrix} \begin{matrix} 1 & 2 \\ 1 & 2 \end{matrix} \end{matrix}) = (\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix})$ .

Step by Step Solution

Step 1: Compute the matrix

Step 2: Apply the application of inverse

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Linear Algebra With Applications

Answers without the blur.

Short Answer

TRUE OR FALSE?There exists a matrix A such that A(1212)=(1111) .

Step by Step Solution

Step 1: Compute the matrix

Step 2: Apply the application of inverse

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

TRUE OR FALSE?
There exists a matrix A such that $A (\begin{matrix} \begin{matrix} 1 & 2 \\ 1 & 2 \end{matrix} \end{matrix}) = (\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix})$ .