Evaluate 2−142.
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Step-by-Step Solution
Step 1: Identify the determinant formula for a 2x2 matrix
To evaluate a 2×2 determinant, we use a specific formula. If the matrix is given as (acbd), its determinant is calculated by multiplying the elements on the main diagonal (a×d) and subtracting the product of the elements on the anti-diagonal (b×c).
Step 2: Identify the elements of the given matrix
From the given determinant 2−142, we can identify the values of a, b, c, and d. Here, a=2, b=4, c=−1, and d=2.
Step 3: Substitute the values into the formula
Now, substitute the identified values of a, b, c, and d into the determinant formula ad - bc. This gives us (2)(2)−(4)(−1).
Step 4: Calculate the products
Perform the multiplications: 2×2=4 and 4×(−1)=−4. So the expression becomes 4−(−4).
Step 5: Simplify the expression
Subtracting a negative number is equivalent to adding its positive counterpart. Therefore, 4−(−4) simplifies to 4+4, which equals 8.