Page 1 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer Page 2 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer XII Here, the two rows R1 and R3 are identical. ? = 0. Question 3: Using the property of determinants and without expanding, prove that: Answer Question 4: Using the property of determinants and without expanding, prove that: Answer Page 3 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer XII Here, the two rows R1 and R3 are identical. ? = 0. Question 3: Using the property of determinants and without expanding, prove that: Answer Question 4: Using the property of determinants and without expanding, prove that: Answer By applying C3 ? C3 + C2, we have: Here, two columns C1 and C3 are proportional. ? = 0. Question 5: Using the property of determinants and without expanding, prove that: Answer Applying R2 ? R2 - R3, we have: Page 4 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer XII Here, the two rows R1 and R3 are identical. ? = 0. Question 3: Using the property of determinants and without expanding, prove that: Answer Question 4: Using the property of determinants and without expanding, prove that: Answer By applying C3 ? C3 + C2, we have: Here, two columns C1 and C3 are proportional. ? = 0. Question 5: Using the property of determinants and without expanding, prove that: Answer Applying R2 ? R2 - R3, we have: Applying R1 ?R3 and R2 ?R3, we have: Applying R1 ? R1 - R3, we have: Applying R1 ?R2 and R2 ?R3, we have: From (1), (2), and (3), we have: Page 5 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer XII Here, the two rows R1 and R3 are identical. ? = 0. Question 3: Using the property of determinants and without expanding, prove that: Answer Question 4: Using the property of determinants and without expanding, prove that: Answer By applying C3 ? C3 + C2, we have: Here, two columns C1 and C3 are proportional. ? = 0. Question 5: Using the property of determinants and without expanding, prove that: Answer Applying R2 ? R2 - R3, we have: Applying R1 ?R3 and R2 ?R3, we have: Applying R1 ? R1 - R3, we have: Applying R1 ?R2 and R2 ?R3, we have: From (1), (2), and (3), we have: Hence, the given result is proved. Question 6: By using properties of determinants, show that: Answer We have, Here, the two rows R1 and R3 are identical. ? = 0.Read More

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