Free Printable WorksheetMathPre-CalculusMath CurriculumHSN-CN.1-9(+)

Pre CAL.142 Find Determinants and Inverses for Two by Two and Three by Three Matrices Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.142 Find Determinants and Inverses for Two by Two and Three by Three Matrices. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.142 Find Determinants and Inverses for Two by Two and Three by Three Matrices - Primary standard selected for prompt fields in this prompt cell: CCSS HSN-CN.1-9(+). Skill statement in this prompt cell: Given a matrix, determine its determinant and whether it is invertible, and select the correct inverse (when it exists). Associated standards listed with this skill in this prompt cell: CCSS HSN-CN.1-9(+); CCSS HSN-VM.1-12(+); SMP 2,4,5,7,8; AP Precalculus CED Unit 4; TX §111.42(c)(3)(I-K); FL MA.912.NSO.2.2-2.5, MA.912.NSO.3; VA MA.AG.3-5. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.142 Find Determinants and Inverses for Two by Two and Three by Three Matrices skill assessments:

Problem 1Difficulty: Mastery
Which 3x3 matrix below is not invertible?
A[[1, 0, 2], [0, 1, 3], [2, 1, 0]] is not invertible.
B[[2, -1, 1], [1, 3, 0], [0, 2, 1]] is not invertible.
C[[3, 0, 1], [1, 1, 0], [0, 2, 2]] is not invertible.
D[[1, 2, 3], [2, 4, 6], [0, 1, 1]] is not invertible.
Solution & Explanation:The matrix [[1, 2, 3], [2, 4, 6], [0, 1, 1]] has row 2 equal to 2 times row 1, so its rows are dependent and its determinant is 0. The other listed matrices have nonzero determinants.
Problem 2Difficulty: Mastery
True or False: For A = [[2, 1, 0], [1, 0, 1], [0, 3, 1]], the matrix B = [[4/7, 1/7, -1/7], [1/7, -2/7, 2/7], [-3/7, 6/7, 1/7]] is A^-1.
ATrue
BFalse
Solution & Explanation:The correct inverse is [[3/7, 1/7, -1/7], [1/7, -2/7, 2/7], [-3/7, 6/7, 1/7]]. Since the proposed B differs from the inverse, multiplying AB would not produce the identity matrix.
Problem 3Difficulty: Mastery
True or False: For A = [[0, 2, 1], [1, 1, 0], [2, 0, 1]], the matrix B = [[-1/4, 1/2, 1/4], [1/4, 1/2, -1/4], [1/2, -1, 1/2]] is A^-1.
ATrue
BFalse
Solution & Explanation:The determinant is -4, so A is invertible. Checking AB gives the identity matrix, so B is A^-1.

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Frequently Asked Questions

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QHow do I download and print this Pre CAL.142 Find Determinants and Inverses for Two by Two and Three by Three Matrices worksheet?

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QIs this Pre CAL.142 Find Determinants and Inverses for Two by Two and Three by Three Matrices worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard HSN-CN.1-9(+) (Primary standard selected for prompt fields in this prompt cell: CCSS HSN-CN.1-9(+). Skill statement in this prompt cell: Given a matrix, determine its determinant and whether it is invertible, and select the correct inverse (when it exists). Associated standards listed with this skill in this prompt cell: CCSS HSN-CN.1-9(+); CCSS HSN-VM.1-12(+); SMP 2,4,5,7,8; AP Precalculus CED Unit 4; TX §111.42(c)(3)(I-K); FL MA.912.NSO.2.2-2.5, MA.912.NSO.3; VA MA.AG.3-5. Use this prompt-provided wording as the supporting standard description for this workflow.).

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