Math / Algebra

QuestionFind the determinant of the following matrix: $\left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]$
0 Part 2 Does this matrix have an inverse? A. Yes B. No Submit entire answer Check parts Next item

Studdy Solution

STEP 1

1. The matrix given is a 2x2 matrix.
2. The determinant of a 2x2 matrix $\left[\begin{array}{cc} a & b \\ c & d \end{array}\right]$ is calculated as $ad - bc$ .
3. A matrix has an inverse if and only if its determinant is non-zero.

STEP 2

1. Calculate the determinant of the matrix.
2. Determine if the matrix has an inverse based on the determinant.

STEP 3

Identify the elements of the matrix:
$\text{Matrix} = \left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]$
Here, $a = 6$ , $b = -2$ , $c = -30$ , and $d = 10$ .

STEP 4

Calculate the determinant using the formula $ad - bc$ :
$\text{Determinant} = (6)(10) - (-2)(-30)$ $= 60 - 60$ $= 0$

STEP 5

Determine if the matrix has an inverse. Since the determinant is zero, the matrix does not have an inverse.
The determinant of the matrix is $0$ .
Part 2 Answer: B. No

Was this helpful?

QuestionFind the determinant of the following matrix: $\left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]$
0 Part 2 Does this matrix have an inverse? A. Yes B. No Submit entire answer Check parts Next item

Studdy Solution

STEP 1

1. The matrix given is a 2x2 matrix.
2. The determinant of a 2x2 matrix $\left[\begin{array}{cc} a & b \\ c & d \end{array}\right]$ is calculated as $ad - bc$ .
3. A matrix has an inverse if and only if its determinant is non-zero.

STEP 2

1. Calculate the determinant of the matrix.
2. Determine if the matrix has an inverse based on the determinant.

STEP 3

Identify the elements of the matrix:
$\text{Matrix} = \left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]$
Here, $a = 6$ , $b = -2$ , $c = -30$ , and $d = 10$ .

STEP 4

Calculate the determinant using the formula $ad - bc$ :
$\text{Determinant} = (6)(10) - (-2)(-30)$ $= 60 - 60$ $= 0$

STEP 5

Determine if the matrix has an inverse. Since the determinant is zero, the matrix does not have an inverse.
The determinant of the matrix is $0$ .
Part 2 Answer: B. No

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the determinant of the following matrix: [6−2−3010]\left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right][6−30​−210​]0 Part 2 Does this matrix have an inverse? A. Yes B. No Submit entire answer Check parts Next item

Studdy Solution

STEP 1

1. The matrix given is a 2x2 matrix.2. The determinant of a 2x2 matrix [abcd]\left[\begin{array}{cc} a & b \\ c & d \end{array}\right][ac​bd​] is calculated as ad−bcad - bcad−bc.3. A matrix has an inverse if and only if its determinant is non-zero.

STEP 2

1. Calculate the determinant of the matrix.2. Determine if the matrix has an inverse based on the determinant.

STEP 3

Identify the elements of the matrix:Matrix=[6−2−3010]\text{Matrix} = \left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]Matrix=[6−30​−210​]Here, a=6a = 6a=6, b=−2b = -2b=−2, c=−30c = -30c=−30, and d=10d = 10d=10.

STEP 4

Calculate the determinant using the formula ad−bcad - bcad−bc:Determinant=(6)(10)−(−2)(−30)\text{Determinant} = (6)(10) - (-2)(-30)Determinant=(6)(10)−(−2)(−30) =60−60= 60 - 60=60−60 =0= 0=0

STEP 5

Determine if the matrix has an inverse. Since the determinant is zero, the matrix does not have an inverse. The determinant of the matrix is 000.Part 2 Answer: B. No

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the determinant of the following matrix: $\left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]$
0 Part 2 Does this matrix have an inverse? A. Yes B. No Submit entire answer Check parts Next item

1. The matrix given is a 2x2 matrix.
2. The determinant of a 2x2 matrix $\left[\begin{array}{cc} a & b \\ c & d \end{array}\right]$ is calculated as $ad - bc$ .
3. A matrix has an inverse if and only if its determinant is non-zero.

1. Calculate the determinant of the matrix.
2. Determine if the matrix has an inverse based on the determinant.

Identify the elements of the matrix:
$\text{Matrix} = \left[\begin{array}{cc} 6 & -2 \\ -30 & 10 \end{array}\right]$
Here, $a = 6$ , $b = -2$ , $c = -30$ , and $d = 10$ .

Calculate the determinant using the formula $ad - bc$ :
$\text{Determinant} = (6)(10) - (-2)(-30)$ $= 60 - 60$ $= 0$

Determine if the matrix has an inverse. Since the determinant is zero, the matrix does not have an inverse.
The determinant of the matrix is $0$ .
Part 2 Answer: B. No