Q4. Find a counterexample to disprov... [FREE SOLUTION]

Chapter 4: Q4. (page 185)

Find a counterexample to disprove the following statement.
Two different matrices can never have the same determinant.

Short Answer

Expert verified

The matrix $A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ and $B [\begin{matrix} 8 & 3 \\ 5 & 2 \end{matrix}]$ disprove the statement 鈥�Two different matrices can never have the same determinant.鈥�.

Step by step solution

- Assume the matrices

In order to disprove the statement 鈥淭wo different matrices can never have the same determinant鈥� consider two $2 脳 2$ matrices $A = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$ and $B [\begin{matrix} 8 & 3 \\ 5 & 2 \end{matrix}]$ and calculate there respective determinants.

-Define a determinant of second order matrix

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $|\begin{matrix} a & b \\ c & d \end{matrix}| = a d - b c$ .

- Find the determinants

Calculate the determinants of matrix A and B and observe if they provide the same value.

$\begin{matrix} | A | = |\begin{matrix} \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \end{matrix}| \\ = 1 脳 (1) 鈭� 0 (0) \\ = 1 \end{matrix}$

And,

$\begin{matrix} | B | = |\begin{matrix} \begin{matrix} 8 & 3 \\ 5 & 2 \end{matrix} \end{matrix}| \\ = 8 脳 (2) 鈭� 3 (5) \\ = 16 鈭� 15 \\ = 1 \end{matrix}$

Clearly, A and B are two different matrices since their corresponding values are different and also they have same determinants which disprove the statement that 鈥淭wo different matrices can never have the same determinant鈥�.

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91影视

Find a counterexample to disprove the following statement.
Two different matrices can never have the same determinant.

Short Answer

Step by step solution

- Assume the matrices

-Define a determinant of second order matrix

- Find the determinants

One App. One Place for Learning.

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91影视

Find a counterexample to disprove the following statement.Two different matrices can never have the same determinant.

Short Answer

Step by step solution

- Assume the matrices

-Define a determinant of second order matrix

- Find the determinants

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Geometry

Decision Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find a counterexample to disprove the following statement.
Two different matrices can never have the same determinant.