StudyGPT Just Leveled Up – Say Hello to Knowee! 🚀
Knowee
Questions
Features
Study Tools

What is the determinant of matrix A=\left[\begin{array}{ccc} 6&9.8\\ {3}&{2}\end{array}\right]?

Question

🧐 Not the exact question you are looking for?Go ask a question

Solution

1. Break Down the Problem

To find the determinant of the given matrix A A , we need to apply the determinant formula for a 2×2 2 \times 2 matrix.

2. Relevant Concepts

The formula for the determinant of a 2×2 2 \times 2 matrix A=[abcd] A = \left[\begin{array}{cc} a & b \\ c & d \end{array}\right] is given by:

det(A)=adbc \text{det}(A) = ad - bc

3. Analysis and Detail

For the matrix A=[69.832] A = \left[\begin{array}{cc} 6 & 9.8 \\ 3 & 2 \end{array}\right] :

  • Identify the elements:

    • a=6 a = 6
    • b=9.8 b = 9.8
    • c=3 c = 3
    • d=2 d = 2
  • Substitute these values into the determinant formula:

det(A)=(6)(2)(9.8)(3) \text{det}(A) = (6)(2) - (9.8)(3)

Calculating each term:

  • (6)(2)=12 (6)(2) = 12
  • (9.8)(3)=29.4 (9.8)(3) = 29.4

Putting it all together:

det(A)=1229.4=17.4 \text{det}(A) = 12 - 29.4 = -17.4

4. Verify and Summarize

The calculations show that the determinant of matrix A A is 17.4 -17.4 .

Final Answer

The determinant of matrix A A is det(A)=17.4 \text{det}(A) = -17.4 .

This problem has been solved

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.