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

NameDate

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

Bo writes A = [1, 2, 0; 3, 1, 2; 0, 1, 1] in a notebook and expands along row 1. What is det(A)?
Esme writes A = [3, 1, 0; 1, 2, 1; 0, 1, 4] in a notebook and expands along row 1. What is det(A)?
3.
Jun needs the inverse of A = [1, 1, 0; 0, 1, 1; 0, 0, 1]. Which is it?
- [−1, −1, 0; 0, −1, −1; 0, 0, −1]
- [1, −1, 0; 0, 1, −1; 0, 0, 1]
- [1, −1, 1; 0, 1, −1; 0, 0, 1]
4.
Kira needs the inverse of A = [1, 0, 0; 2, 1, 0; 0, 3, 1]. Which is it?
- [1, 0, 0; −2, 1, 0; 6, −3, 1]
- [1, 0, 0; −2, 1, 0; 0, −3, 1]
- [1, 0, 0; 2, 1, 0; 0, 3, 1]
5.
Luz needs the inverse of A = [1, 0, 0; 0, −1, 0; 0, 0, 1]. Which is it?
- It has no inverse
- [−1, 0, 0; 0, 1, 0; 0, 0, −1]
- Matrix A, unchanged
6.
Does Milo's A = [1, 2, 3; 4, 5, 6; 7, 8, 9] have an inverse?
- Yes: no row is made of zeros
- Yes: det(A) = 45
- No: det(A) = 0
7.
Does Noah's A = [2, 0, 0; 0, 3, 0; 0, 0, 0] have an inverse?
- Yes: det(A) = 5
- No: det(A) = 0
- Yes: det(A) = 6
8.
What sign goes with the entry in row 2, column 1 when Ren expands?
- ×
- +
- −
9.
Why does Tala expand along a row with zeros?
- Zeros make det = 0
- Zero entries drop their terms
- Zeros flip each sign
10.
Zee swaps two rows of a matrix with det 7. What is the new determinant?
- 0
- −7
- 7

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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