Calculate the determinant | 2 3 | | 4 5 | + | 1 1 | | 1 1 |.

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Question: Calculate the determinant | 2 3 | | 4 5 | + | 1 1 | | 1 1 |.

Options:

Correct Answer: 1

Solution:

The first determinant is -2 and the second is 0, so the total is -2 + 0 = -2.

Calculate the determinant | 2 3 | | 4 5 | + | 1 1 | | 1 1 |.

Calculate the determinant | 2 3 | | 4 5 | + | 1 1 | | 1 1 |.

Correct Answer: -2

Step 1: Identify the first determinant, which is | 2 3 | | 4 5 |.
Step 2: Calculate the first determinant using the formula: (a*d) - (b*c), where a=2, b=3, c=4, d=5.
Step 3: Substitute the values into the formula: (2*5) - (3*4).
Step 4: Calculate 2*5 = 10 and 3*4 = 12.
Step 5: Now subtract: 10 - 12 = -2. So, the first determinant is -2.
Step 6: Identify the second determinant, which is | 1 1 | | 1 1 |.
Step 7: Calculate the second determinant using the same formula: (a*d) - (b*c), where a=1, b=1, c=1, d=1.
Step 8: Substitute the values into the formula: (1*1) - (1*1).
Step 9: Calculate 1*1 = 1 and 1*1 = 1.
Step 10: Now subtract: 1 - 1 = 0. So, the second determinant is 0.
Step 11: Add the two determinants together: -2 + 0.
Step 12: Calculate the total: -2 + 0 = -2.

Determinants of 2x2 Matrices – The determinant of a 2x2 matrix | a b | | c d | is calculated as ad - bc.
Addition of Determinants – The question involves adding the results of two separate determinants.