Q3. Explain why聽2173鈭�50聽doesn鈥�... [FREE SOLUTION]

Chapter 4: Q3. (page 185)

Explain why $[\begin{matrix} 2 & 1 & 7 \\ 3 & 鈭� 5 & 0 \end{matrix}]$ doesn鈥檛 have a determinant.

Short Answer

Expert verified

The matrix $[\begin{matrix} 2 & 1 & 7 \\ 3 & 鈭� 5 & 0 \end{matrix}]$ is not a square matrix and so as per the definition of the determinant, the matrix will not have a determinant.

Step by step solution

- Define a determinant of a matrix

A determinant is a number obtained by solving a square matrix only by certain methods which tells us about certain properties of the respective matrix.

- 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., $|\begin{matrix} a & b \\ c & d \end{matrix}| = a d 鈭� b c$ .

For example: Apply the definition of the method of finding determinant of second order matrix $|\begin{matrix} 8 & 3 \\ 鈭� 5 & 2 \end{matrix}|$ .

$\begin{matrix} |\begin{matrix} 8 & 3 \\ 鈭� 5 & 2 \end{matrix}| = 8 脳 (2) 鈭� 3 (鈭� 5) \\ = 16 + 15 \\ = 31 \end{matrix}$

- State the conclusion

Since $[\begin{matrix} 2 & 1 & 7 \\ 3 & 鈭� 5 & 0 \end{matrix}]$ is the matrix of order $2 脳 3$ , therefore the given matrix is not a square matrix and so as per the definition of the determinant, the matrix will not have one.

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Explain why $[\begin{matrix} 2 & 1 & 7 \\ 3 & 鈭� 5 & 0 \end{matrix}]$ doesn鈥檛 have a determinant.

Short Answer

Step by step solution

- Define a determinant of a matrix

- Define a determinant of second order matrix

- State the conclusion

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91影视

Explain why2173鈭�50doesn鈥檛 have a determinant.

Short Answer

Step by step solution

- Define a determinant of a matrix

- Define a determinant of second order matrix

- State the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Pure Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Explain why $[\begin{matrix} 2 & 1 & 7 \\ 3 & 鈭� 5 & 0 \end{matrix}]$ doesn鈥檛 have a determinant.