Grade 11 · Math · Algebra 2

11th grade Determinants and inverse matrices worksheet

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Determinants and inverse matrices

Grade 11 Math Worksheet - Challenge Me

NameDate

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

1.
Noah unscrambles a message coded with A = [3, -2; 4, 1]. What is A⁻¹?
- (1/11)[1, -2; 4, 3]
- (1/5)[-1, -2; 4, -3]
- [1, 2; -4, 3]
- (1/11)[1, 2; -4, 3]
- (1/11)[3, 2; -4, 1]
2.
Pia checks the table A = [-2, 6; 1, -3] for a puzzle card. What is A⁻¹?
- No inverse: det(A) = 0
- (1/12)[-3, -6; -1, -2]
- [-3, 6; 1, -2]
- [-3, -6; -1, -2]
3.
Ren works out the inverse of A = [2, 5; 1, -2] on a worksheet. What is A⁻¹?
- (1/9)[-2, 5; 1, 2]
- (1/9)[2, 5; 1, -2]
- [-2, -5; -1, 2]
- (1/9)[2, -5; -1, -2]
4.
Tala checks the table A = [6, -4; -3, 2] for a puzzle card. What is A⁻¹?
- No inverse: det(A) = 0
- [2, 4; 3, 6], ignoring the determinant
- [2, -4; -3, 6]
- (1/24)[2, 4; 3, 6]
Bo wants the table A = [5, k; 3, 6] to have no inverse. What value of k makes that happen?
Esme wants the table A = [2, 9; 4, k] to have no inverse. What value of k makes that happen?
Jun wants the table A = [9, 6; k, 2] to have no inverse. What value of k makes that happen?
Luz reshapes a 2-by-2 rug square with M = [4, 1; 2, -1]. What is the area of the image, in square units?
Noah reshapes a 1-by-3 quilt strip with M = [3, 2; 1, -2]. What is the area of the image, in square units?
Pia reshapes a 4-by-1 rug strip with M = [1, 3; 2, 1]. What is the area of the image, in square units?

Determinants and inverse matrices. Every version has 10 questions, and the answer key prints on the second page.

I can find the determinant of a 2-by-2 matrix: the down product minus the up product.
I can tell whether a matrix has an inverse, and find the inverse by swapping, changing signs and dividing by the determinant.
I can find the entry that makes a matrix have no inverse, and use |det| to find the area of a stretched shape.

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

matrix: A table of numbers in rows and columns, like [3, 1; 5, 2].

entry: One number in a matrix, named by its row and column.

determinant, det(A): For [a, b; c, d], the number ad − bc.

down / up diagonal: Top left to bottom right / bottom left to top right.

identity matrix, I: [1, 0; 0, 1]: multiplying by it changes nothing.

inverse, A⁻¹: The matrix that undoes A, so A × A⁻¹ = I.

Added the two diagonal products instead of subtracting them. Work out one 2-by-2 together: the down product minus the up product.

Took the down product away from the up product, so the sign came out flipped. Ask which diagonal starts at the top left.

Multiplied along the rows instead of the diagonals. Trace the two diagonals of a 2-by-2 table with a finger together.

What is the most common mistake with determinants and inverse matrices?

Added the two diagonal products instead of subtracting them. Work out one 2-by-2 together: the down product minus the up product.

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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