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Lesson Worksheet: Inverse of a Matrix: The Adjoint Method Mathematics • 10th Grade

In this worksheet, we will practice finding the inverse of 3 × 3 matrices using the adjoint method.

Q1:

Find the cofactor matrix of 𝐴=758372048.

  • A48846245638122864
  • B758372048
  • C48241285628463864
  • D48241285628463864

Q2:

Find the adjoint matrix of the matrix 𝐴=272979854.

  • A73187736801014677
  • B73187736801014677
  • C73361011884677077
  • D272979854

Q3:

Find the multiplicative inverse of the matrix 500050005.

  • A1125250002500025
  • B250002500025
  • C1125250002500025
  • D250002500025

Q4:

True or False: If 𝐴 is any given square matrix of order 𝑛, then 𝐴×(𝐴)=(𝐴)×𝐴=|𝐴|𝐼adjadj, where 𝐼 is the identity matrix of order 𝑛.

  • AFalse
  • BTrue

Q5:

Consider the matrix 𝐴=2140530010. Find its inverse, given that it has the form 𝐴=𝑋𝑝𝑞0𝑌𝑟00𝑍, where 𝑋, 𝑌, 𝑍, 𝑝, 𝑞, and 𝑟 are numbers you should find.

  • A𝐴=141120161300110
  • B𝐴=141120131500110
  • C𝐴=121140151300110
  • D𝐴=121101710001535000110
  • E𝐴=121130161300110

Q6:

Consider the matrix 103101310. Determine whether the matrix has an inverse by finding whether the determinant is nonzero. If the determinant is nonzero, find the inverse using the formula for the inverse which involves the cofactor matrix.

  • AThere is no inverse because its determinant equals zero.
  • BIt has an inverse, which is 123212329212010.
  • CIt has an inverse, which is 123203292112120.
  • DIt has an inverse, which is 131391020.
  • EIt has an inverse, which is 130392110.

Q7:

Suppose that 𝐴𝑋=𝐵, where 𝐴=413504332,𝐵=210345276,

and 𝑋 is a 3×3 matrix.

Calculate the inverse of 𝐴 and use it to find 𝑋.

  • A5121111171615
  • B2232411108
  • C11292318332412927
  • D11292318332412927
  • E5121111171615

Q8:

Determine whether the matrix 123021267 has an inverse by finding whether the determinant is nonzero. If the determinant is nonzero, find the inverse using the inverse formula involving the cofactor matrix.

  • AThere is no inverse because the determinant equals zero.
  • B824412412
  • C824412412
  • D844211422
  • E844211422

Q9:

Consider the matrix 103101310. Determine whether the matrix has an inverse by finding whether the determinant is nonzero. If the determinant is nonzero, find the inverse using the formula for the inverse which involves the cofactor matrix.

  • AIt has an inverse, which is 123212329212010.
  • BIt has an inverse, which is 130392110.
  • CIt has an inverse, which is 131391020.
  • DIt has an inverse, which is 123203292112120.
  • EThere is no inverse because its determinant equals zero.

Q10:

Find the inverse of the matrix 𝑒𝑡𝑡𝑒𝑡𝑡𝑒𝑡𝑡.cossinsincoscossin

  • A𝑒0𝑒(𝑡+𝑡)2𝑡(𝑡𝑡)(𝑡𝑡)2𝑡(𝑡+𝑡)sincossinsincossincoscossincos
  • B12𝑒012𝑒12(𝑡+𝑡)𝑡𝑡12(𝑡𝑡)𝑡12(𝑡+𝑡)sincossincossincoscossincos
  • C12𝑒012𝑒12(𝑡+𝑡)𝑡12(𝑡𝑡)12(𝑡𝑡)𝑡12(𝑡+𝑡)sincossinsincossincoscossincos
  • D12𝑒12(𝑡+𝑡)12(𝑡𝑡)0𝑡𝑡12𝑒12(𝑡𝑡)12(𝑡+𝑡)sincossincossincossincossincos
  • E𝑒(𝑡+𝑡)(𝑡𝑡)02𝑡2𝑡𝑒(𝑡𝑡)(𝑡+𝑡)sincossincossincossincossincos

This lesson includes 42 additional questions and 117 additional question variations for subscribers.

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