Math  /  Algebra

QuestionFind the determinant of the matrix. [29106]\left[\begin{array}{cc} 2 & 9 \\ 10 & 6 \end{array}\right]

Studdy Solution

STEP 1

What is this asking? We need to find a single number that represents a special value associated with this 2×22 \times 2 matrix, called its determinant. Watch out! Don't mix up the order of the numbers when multiplying and subtracting!

STEP 2

1. Set up the determinant formula
2. Calculate the determinant

STEP 3

The determinant of a 2×22 \times 2 matrix [abcd]\begin{bmatrix} a & b \\ c & d \end{bmatrix} is calculated as adbcad - bc.
This formula is **super important** to remember!

STEP 4

In our matrix, we have a=2a = 2, b=9b = 9, c=10c = 10, and d=6d = 6.
Let's **plug these values** into our determinant formula!

STEP 5

We multiply aa and dd: 26=122 \cdot 6 = 12.
This is the product of the **main diagonal**.

STEP 6

Next, we multiply bb and cc: 910=909 \cdot 10 = 90.
This is the product of the **other diagonal**.

STEP 7

Finally, we **subtract** the second product from the first: 1290=7812 - 90 = -78.
So, the **determinant** of our matrix is 78-78!

STEP 8

The determinant of the matrix is 78-78.

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