Question: Calculate the determinant \\( \\begin{vmatrix} a & b \\\\ c & d \\end{vmatrix} \\)
Options:
ad - bc
ab + cd
ac - bd
bc - ad
Correct Answer: ad - bc
Solution:
The determinant is calculated as \\( ad - bc \\).
Calculate the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix
Practice Questions
Q1
Calculate the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \)
ad - bc
ab + cd
ac - bd
bc - ad
Questions & Step-by-Step Solutions
Calculate the determinant \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \)
Step 1: Identify the elements of the 2x2 matrix. The matrix is given as \( \begin{vmatrix} a & b \\ c & d \end{vmatrix} \). Here, 'a' is the top left element, 'b' is the top right element, 'c' is the bottom left element, and 'd' is the bottom right element.
Step 2: Multiply the top left element 'a' by the bottom right element 'd'. This gives you the product \( ad \).
Step 3: Multiply the top right element 'b' by the bottom left element 'c'. This gives you the product \( bc \).
Step 4: Subtract the result from Step 3 from the result from Step 2. This means you calculate \( ad - bc \).
Step 5: The result from Step 4 is the determinant of the matrix.
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