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1 2 Let A be the matrix |7 8 3 6 5 4 (a) Write out the cofactor expansion of det A along the first row. (This should be a sum/difference of three 2 x 2 determinants multiplied by constants. For this part, do not evaluate the 2 x 2 determinants.) (b) Repeat part (a), but for the cofactor expansion along the second column. (c) Compute det A using one of the cofactor expansions you found in parts (a) and (b). (d) If B is a 3 × 3 matrix such that det B = 6, and C is the matrix obtained from B by switching its first two rows, what is det(6AC¬1)?

1 2 Let A be the matrix |7 8 3 6 5 4 (a) Write out the cofactor expansion of det A along the first row. (This should be a sum/difference of three 2 x 2 determinants multiplied by constants. For this part, do not evaluate the 2 x 2 determinants.) (b) Repeat part (a), but for the cofactor expansion along the second column. (c) Compute det A using one of the cofactor expansions you found in parts (a) and (b). (d) If B is a 3 × 3 matrix such that det B = 6, and C is the matrix obtained from B by switching its first two rows, what is det(6AC¬1)?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Please explain part b,c and d. (I have attached an answer key)

For part (b), the cofactor expansion along the second column is [o 1 det 7 8 3 6 5 4 3] +8 det 6 det A = -1 det 5 det For part (c), evaluating one of the right-hand-side expressions above (part (a) is easier, since one of the coefficients is 0) gives det A various properties of determinants. : -36. For part (d), det(6AC-1) = 6³ · (-36) · (-¿) = 1296 using the
Transcribed Image Text:For part (b), the cofactor expansion along the second column is [o 1 det 7 8 3 6 5 4 3] +8 det 6 det A = -1 det 5 det For part (c), evaluating one of the right-hand-side expressions above (part (a) is easier, since one of the coefficients is 0) gives det A various properties of determinants. : -36. For part (d), det(6AC-1) = 6³ · (-36) · (-¿) = 1296 using the
1 2 Let A be the matrix |7 8 3 6 5 4 (a) Write out the cofactor expansion of det A along the first row. (This should be a sum/difference of three 2 x 2 determinants multiplied by constants. For this part, do not evaluate the 2 x 2 determinants.) (b) Repeat part (a), but for the cofactor expansion along the second column. (c) Compute det A using one of the cofactor expansions you found in parts (a) and (b). (d) If B is a 3 × 3 matrix such that det B = 6, and C is the matrix obtained from B by switching its first two rows, what is det(6AC¬1)?
Transcribed Image Text:1 2 Let A be the matrix |7 8 3 6 5 4 (a) Write out the cofactor expansion of det A along the first row. (This should be a sum/difference of three 2 x 2 determinants multiplied by constants. For this part, do not evaluate the 2 x 2 determinants.) (b) Repeat part (a), but for the cofactor expansion along the second column. (c) Compute det A using one of the cofactor expansions you found in parts (a) and (b). (d) If B is a 3 × 3 matrix such that det B = 6, and C is the matrix obtained from B by switching its first two rows, what is det(6AC¬1)?
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