Find the determinant of G = [[1, 2], [2, 4]]. (2020)
Practice Questions
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Find the determinant of G = [[1, 2], [2, 4]]. (2020)
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Questions & Step-by-Step Solutions
Find the determinant of G = [[1, 2], [2, 4]]. (2020)
Step 1: Identify the matrix G, which is [[1, 2], [2, 4]].
Step 2: Write down the formula for the determinant of a 2x2 matrix, which is: det(G) = (a*d) - (b*c), where G = [[a, b], [c, d]].
Step 3: Assign the values from the matrix G to the variables: a = 1, b = 2, c = 2, d = 4.
Step 4: Substitute the values into the determinant formula: det(G) = (1*4) - (2*2).
Step 5: Calculate the first part: 1*4 = 4.
Step 6: Calculate the second part: 2*2 = 4.
Step 7: Subtract the second part from the first part: 4 - 4 = 0.
Step 8: Conclude that the determinant of G is 0.
Determinant Calculation – The determinant of a 2x2 matrix is calculated using the formula ad - bc, where the matrix is represented as [[a, b], [c, d]].
Matrix Properties – Understanding that the determinant can indicate properties of the matrix, such as whether it is invertible (non-zero determinant) or singular (zero determinant).
