Podcast
Questions and Answers
What must be true for the determinant | b+c c+a a+b | | c+a a+b b+c | | a+b b+c c+a | to not be equal to zero?
What must be true for the determinant | b+c c+a a+b | | c+a a+b b+c | | a+b b+c c+a | to not be equal to zero?
- a, b, c are all equal
- a + b + c = 0 (correct)
- abc = 0 (correct)
- a, b, c are all positive (correct)
In the expression | 1 + a 1 1 | = abc (1 + 1/a + 1/b + 1/c), what is assumed about a, b, and c?
In the expression | 1 + a 1 1 | = abc (1 + 1/a + 1/b + 1/c), what is assumed about a, b, and c?
- They are all positive. (correct)
- They can be any real numbers. (correct)
- They are irrational numbers. (correct)
- They must all be negative. (correct)
What conclusion can be drawn if | 1 logb logc | | loga 1 logc | = 0?
What conclusion can be drawn if | 1 logb logc | | loga 1 logc | = 0?
- At least one of a, b, c must be zero. (correct)
- a, b, c are non-negative.
- At least one of a, b, or c equals 1. (correct)
- loga, logb and logc are all equal.
Which of the following equations could be solved using Cramer's rule?
Which of the following equations could be solved using Cramer's rule?
What does the determinant | 1 a a^2 | | 1 b b^2 | | 1 c c^2 | equal if shown without expanding?
What does the determinant | 1 a a^2 | | 1 b b^2 | | 1 c c^2 | equal if shown without expanding?
If | 3 2 4 | = | 2 x 3 |, what is the value of x? | 1 2 7 |
If | 3 2 4 | = | 2 x 3 |, what is the value of x? | 1 2 7 |
For the determinant | 2ab^2 a b | | a^2 b 2ab | | b^2 2ab a |, which identity holds true?
For the determinant | 2ab^2 a b | | a^2 b 2ab | | b^2 2ab a |, which identity holds true?
Which expression is equivalent to the determinant | x-1 1 1 | if the determinant equals 0? | 1 x+1 -1 | | -1 1 x+1 |
Which expression is equivalent to the determinant | x-1 1 1 | if the determinant equals 0? | 1 x+1 -1 | | -1 1 x+1 |
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Study Notes
### Determinant Year Wise Questions
- Year 2023:
- Calculate determinant of a 3x3 matrix
- Prove that the determinant of a 3x3 matrix is equal to 0
- In another question, prove that either a + b + c = 0 or abc = 0 if the determinant of a certain 3x3 matrix is not equal to 0
- Year 2022:
- Prove that the determinant of a 3x3 matrix is equal to abc(1 + 1/a + 1/b + 1/c)
- In another question, prove that the determinant is equal to (1 - x)^3
- Solve for x if two determinant equations are equal
- Year 2020:
- Prove that the determinant of a certain 3x3 matrix is equal to 0
- Prove that 1 + xyz = 0 if certain x, y, z values are known
- In another question, prove that the determinant is equal to (1 - x)^3
- Year 2019:
- Solve for x when two determinant equations are equal
- Prove that the determinant of a 3x3 matrix is equal to 2abc(1 + 1/a + 1/b + 1/c)
- Solve a system of linear equations using Cramer's rule
- Year 2018:
- Prove that the determinant of a certain 3x3 matrix is equal to (a+b)(b-c)(c-a) without expanding the determinant
- Solve for x if the determinant equation is equal to 0
- Prove that the determinant of a certain 3x3 matrix is equal to (ab+bc+ca)²
- Year 2017:
- Prove that the determinant of a certain 3x3 matrix is equal to 0
- Solve a system of linear equations using Cramer's rule
- Prove that the determinant of a certain 3x3 matrix is equal to (a² + b² )²
- Prove that the determinant of a certain 3x3 matrix is divisible by 100 without expanding the determinant
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