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

1. Break Down the Problem

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

2. Relevant Concepts

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

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

3. Analysis and Detail

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

• Identify the elements:

  • $a = 6$
  • $b = 9.8$
  • $c = 3$
  • $d = 2$

• Substitute these values into the determinant formula:

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

Calculating each term:

• $(6)(2) = 12$
• $(9.8)(3) = 29.4$

Putting it all together:

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

4. Verify and Summarize

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

Final Answer

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