Grade 11 · Math · Algebra 2

11th grade Determinants and inverse matrices worksheet

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Determinants and inverse matrices

Grade 11 Math Worksheet - Building Confidence

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Number table A, 2 by 2
Row 1 is 6, 1; row 2 is 3, 4. The down diagonal (6 to 4) is blue; the up diagonal (3 to 1) is orange.
Jun copies matrix A = [6, 1; 3, 4] from the board. The down diagonal gives 6 × 4 and the up diagonal gives 1 × 3. What is det(A)?
Number table A, 2 by 2
Row 1 is 7, 3; row 2 is 2, 5. The down diagonal (7 to 5) is blue; the up diagonal (2 to 3) is orange.
Kira reads matrix A = [7, 3; 2, 5] in a math book. The down diagonal gives 7 × 5 and the up diagonal gives 3 × 2. What is det(A)?
Luz checks matrix A = [8, 3; 5, 2] on a worksheet. What is det(A)?
Milo writes matrix A = [4, 7; 1, 3] for a homework problem. What is det(A)?
A⁻¹ = (1/det(A)) × [d, -b; -c, a]
Swap the down diagonal, change the signs of the up diagonal, then divide every entry by det(A).
Pia finds the inverse of A = [5, 2; 3, 4], and det(A) = 14. What is the top-right entry of A⁻¹?
Ren finds the inverse of A = [7, 2; 3, 4], and det(A) = 22. What is the bottom-left entry of A⁻¹?
Tala finds the inverse of A = [5, 3; 4, 6], and det(A) = 18. What is the top-left entry of A⁻¹?
Zee finds the inverse of A = [2, 5; 1, 4], and det(A) = 3. What is the top-left entry of A⁻¹?
Esme finds the inverse of A = [6, 4; 1, 3], and det(A) = 14. What is the bottom-right entry of A⁻¹?
10.
Jun wants to decode messages coded with the table A = [6, 4; 9, 6]. Does A have an inverse?
- Yes: det(A) = 0
- Yes: det(A) = 72
- No: det(A) = 0
- Yes: det(A) = -30

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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