Math / Algebra

QuestionEvaluate the determinant. $\begin{array}{l} \left|\begin{array}{ll} 9 & 3 \\ 2 & 8 \end{array}\right| \\ \left|\begin{array}{ll} 9 & 3 \\ 2 & 8 \end{array}\right|= \end{array}$

Studdy Solution

STEP 1

1. The determinant is for a $2 \times 2$ matrix.
2. The formula for the determinant of a $2 \times 2$ matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is $ad - bc$ .

STEP 2

1. Identify the elements of the matrix.
2. Apply the determinant formula.
3. Calculate the determinant.

STEP 3

Identify the elements of the matrix $\begin{pmatrix} 9 & 3 \\ 2 & 8 \end{pmatrix}$ :
- $a = 9$ - $b = 3$ - $c = 2$ - $d = 8$

STEP 4

Apply the determinant formula for a $2 \times 2$ matrix, which is $ad - bc$ .
$\text{Determinant} = (9)(8) - (3)(2)$

STEP 5

Calculate the determinant:
$\text{Determinant} = 72 - 6$ $\text{Determinant} = 66$
The determinant of the matrix is:
$\boxed{66}$

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QuestionEvaluate the determinant. $\begin{array}{l} \left|\begin{array}{ll} 9 & 3 \\ 2 & 8 \end{array}\right| \\ \left|\begin{array}{ll} 9 & 3 \\ 2 & 8 \end{array}\right|= \end{array}$

Studdy Solution

STEP 1

1. The determinant is for a $2 \times 2$ matrix.
2. The formula for the determinant of a $2 \times 2$ matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is $ad - bc$ .

STEP 2

1. Identify the elements of the matrix.
2. Apply the determinant formula.
3. Calculate the determinant.

STEP 3

Identify the elements of the matrix $\begin{pmatrix} 9 & 3 \\ 2 & 8 \end{pmatrix}$ :
- $a = 9$ - $b = 3$ - $c = 2$ - $d = 8$

STEP 4

Apply the determinant formula for a $2 \times 2$ matrix, which is $ad - bc$ .
$\text{Determinant} = (9)(8) - (3)(2)$

STEP 5

Calculate the determinant:
$\text{Determinant} = 72 - 6$ $\text{Determinant} = 66$
The determinant of the matrix is:
$\boxed{66}$

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QuestionEvaluate the determinant. ∣9328∣∣9328∣=\begin{array}{l} \left|\begin{array}{ll} 9 & 3 \\ 2 & 8 \end{array}\right| \\ \left|\begin{array}{ll} 9 & 3 \\ 2 & 8 \end{array}\right|= \end{array}∣∣​92​38​∣∣​∣∣​92​38​∣∣​=​

Studdy Solution

STEP 1

1. The determinant is for a 2×22 \times 22×2 matrix.2. The formula for the determinant of a 2×22 \times 22×2 matrix (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}(ac​bd​) is ad−bcad - bcad−bc.

STEP 2

1. Identify the elements of the matrix.2. Apply the determinant formula.3. Calculate the determinant.

STEP 3

Identify the elements of the matrix (9328)\begin{pmatrix} 9 & 3 \\ 2 & 8 \end{pmatrix}(92​38​):- a=9a = 9a=9 - b=3b = 3b=3 - c=2c = 2c=2 - d=8d = 8d=8

STEP 4

Apply the determinant formula for a 2×22 \times 22×2 matrix, which is ad−bcad - bcad−bc.Determinant=(9)(8)−(3)(2) \text{Determinant} = (9)(8) - (3)(2) Determinant=(9)(8)−(3)(2)

STEP 5

Calculate the determinant:Determinant=72−6 \text{Determinant} = 72 - 6 Determinant=72−6 Determinant=66 \text{Determinant} = 66 Determinant=66 The determinant of the matrix is:66 \boxed{66} 66​

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QuestionEvaluate the determinant. $\begin{array}{l} \left|\begin{array}{ll} 9 & 3 \\ 2 & 8 \end{array}\right| \\ \left|\begin{array}{ll} 9 & 3 \\ 2 & 8 \end{array}\right|= \end{array}$

1. The determinant is for a $2 \times 2$ matrix.
2. The formula for the determinant of a $2 \times 2$ matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is $ad - bc$ .

1. Identify the elements of the matrix.
2. Apply the determinant formula.
3. Calculate the determinant.

Identify the elements of the matrix $\begin{pmatrix} 9 & 3 \\ 2 & 8 \end{pmatrix}$ :
- $a = 9$ - $b = 3$ - $c = 2$ - $d = 8$

Apply the determinant formula for a $2 \times 2$ matrix, which is $ad - bc$ .
$\text{Determinant} = (9)(8) - (3)(2)$

Calculate the determinant:
$\text{Determinant} = 72 - 6$ $\text{Determinant} = 66$
The determinant of the matrix is:
$\boxed{66}$