
Finding Determinant & Inverse of Matrices Flashcard

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the determinant of a 2x2 matrix?
Back
For a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), the determinant is calculated as \( det(A) = ad - bc \).
2.
FLASHCARD QUESTION
Front
How do you find the inverse of a 2x2 matrix?
Back
For a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), the inverse is given by \( A^{-1} = \frac{1}{det(A)} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} \) if \( det(A) \neq 0 \).
3.
FLASHCARD QUESTION
Front
Calculate the determinant of the matrix \( \begin{pmatrix} 3 & 2 \\ 1 & 4 \end{pmatrix} \).
Back
The determinant is \( det = (3)(4) - (2)(1) = 12 - 2 = 10 \).
4.
FLASHCARD QUESTION
Front
What is the determinant of the matrix \( \begin{pmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{pmatrix} \)?
Back
The determinant is calculated using cofactor expansion or row reduction. The answer is -24.
5.
FLASHCARD QUESTION
Front
What does it mean if the determinant of a matrix is zero?
Back
If the determinant of a matrix is zero, it means the matrix is singular and does not have an inverse.
6.
FLASHCARD QUESTION
Front
How do you evaluate the determinant of a 3x3 matrix?
Back
For a 3x3 matrix \( A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} \), the determinant is \( det(A) = a(ei - fh) - b(di - fg) + c(dh - eg) \).
7.
FLASHCARD QUESTION
Front
What is the formula for the determinant of a 2x2 matrix?
Back
For a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), the formula is \( det(A) = ad - bc \).
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