Grade 11 · Math · Algebra 2

11th grade Determinants and inverses of 3 by 3 matrices worksheet

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Determinants and inverses of 3 by 3 matrices

Grade 11 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Bo's 3 by 3 matrices have det(A) = -2 and det(B) = 7. A code is made by multiplying them. What is det(AB)?
Esme's 3 by 3 matrices have det(A) = 8 and det(B) = 0.25. A code is made by multiplying them. What is det(AB)?
3.
Jun solves Ax = (6, 3, 2) with A⁻¹ = [1, −1, 1; 0, 1, −1; 0, 0, 1]. What is x?
- (11, 5, 2)
- (6, 3, 2)
- (5, 1, 2)
4.
Kira's 3 by 3 matrix A has det(A) = 5. What is det(2A)?
- 10
- 40
- 20
5.
Luz's matrix has det(A) = 4. What is det(A⁻¹)?
- −4
- 4
- 1/4
6.
Noah gets 23 for det [2, 1, 3; 0, 4, 1; 1, 2, 5] by adding all three terms. Agree or disagree?
- Agree: 23 is the sum of entries
- Disagree: it is 25
- Agree: adding the terms is right
7.
Pia says a matrix with a zero entry can't have an inverse. Agree or disagree?
- Agree: a zero breaks the inverse
- Disagree: only det = 0 rules it out
- Agree: zeros make det 0
8.
Which of Ren's matrices has no inverse?
- [1, 0, 0; 0, 2, 0; 0, 0, 3]
- [1, 2, 3; 2, 4, 6; 0, 1, 1]
- [1, 2, 3; 0, 4, 6; 0, 0, 1]
9.
Which of Tala's matrices has determinant 1?
- [1, 4, 2; 0, 1, 3; 0, 0, 1]
- [1, 4, 2; 0, 0, 3; 0, 0, 1]
- [2, 4, 2; 0, 1, 3; 0, 0, 1]
10.
Zee's matrix has det 3. How does it change the volume of a cube it transforms?
- It cubes the volume
- It triples the volume
- It adds 3 to the volume

Determinants and inverses of 3 by 3 matrices. Every version has 10 questions, and the answer key prints on the second page.

Standard: N-VM.C.10 (+), N-VM.C.12 (+)

determinant: A number from a square table; 0 means no inverse

minor: The 2 by 2 determinant left after crossing out a row and column

cofactor sign: + or − from a checkerboard, + in the top left

identity I: 1s on the diagonal and 0s elsewhere

inverse A⁻¹: The table with A × A⁻¹ = I

Your child added the diagonal numbers. For a triangular matrix the determinant is the product of the diagonal.

Your child added all three terms. Along row 1 the signs go +, −, +, so the middle term is subtracted.

Your child added the determinants. The determinant of a product is the product of the determinants.

What is the most common mistake with determinants and inverses of 3 by 3 matrices?

Your child added the diagonal numbers. For a triangular matrix the determinant is the product of the diagonal.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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