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Let A be a nonsingular n x n matrix, with n ≥ 2. Prove the following formula. ladj(A)| = |A|-1 Since A is nonsingular, we know that A. adj(A) = |AT|A B.O adj(A) = |A|AT C. adj(A) = |A¹|A D.O adj(A) = 0 E. O adj(A) = |A|A-1 -Select--- |adj(A)| = |AI|A-¹1 BO ladj(A)| = |A|-|A| C.O ladj(A)| = |A|^|A| DO ladj(A)| = |A|¹|A| E.O ladj(A)| = |A|A| To conclude, we apply ---Select--- --Select--- A is invertible A has an entire row consisting of zeros A is equal to its transpose the determinant of A is zero Taking the determinant of both sides of this equality and applying the property of a scalar multiple of a matrix gives which of the following? A.o Thus, we can express the adjoint of A as which of the following? ✓ ---Select--- the determinant of an inverse matrix property the determinant of a transpose property the determinant of a matrix product property Cramer's Rule ✓and simplify to achieve the equation |adj(A)| = |A|^ − 1.

Let A be a nonsingular n x n matrix, with n ≥ 2. Prove the following formula. ladj(A)| = |A|-1 Since A is nonsingular, we know that A. adj(A) = |AT|A B.O adj(A) = |A|AT C. adj(A) = |A¹|A D.O adj(A) = 0 E. O adj(A) = |A|A-1 -Select--- |adj(A)| = |AI|A-¹1 BO ladj(A)| = |A|-|A| C.O ladj(A)| = |A|^|A| DO ladj(A)| = |A|¹|A| E.O ladj(A)| = |A|A| To conclude, we apply ---Select--- --Select--- A is invertible A has an entire row consisting of zeros A is equal to its transpose the determinant of A is zero Taking the determinant of both sides of this equality and applying the property of a scalar multiple of a matrix gives which of the following? A.o Thus, we can express the adjoint of A as which of the following? ✓ ---Select--- the determinant of an inverse matrix property the determinant of a transpose property the determinant of a matrix product property Cramer's Rule ✓and simplify to achieve the equation |adj(A)| = |A|^ − 1.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 30E
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Let A be a nonsingular n x n matrix, with n ≥ 2. Prove the following formula. |adj(A)| = |A|-1 Since A is nonsingular, we know that ---Select--- A. adj(A) = |AT|A B. O adj(A) = |A|AT C. adj(A) = |A¹|A D.O adj(A) = 0 E. adj(A) = |A|A-1 = ---Select--- A is invertible A has an entire row consisting of zeros. A is equal to its transpose the determinant of A is zero Taking the determinant of both sides of this equality and applying the property of a scalar multiple of a matrix gives which of the following? A.O ladj(A)I = = |A||A¹| BO ladj(A)| = |A|-^|A| В C.O ladj(A)| = |A||A| DO ladj(A): |A|-¹|A| O E. ladj(A)| = |A|T|A| To conclude, we apply |---Select--- ---Select--- Thus, we can express the adjoint of A as which of the following? the determinant of an inverse matrix property the determinant of a transpose property. the determinant of a matrix product property Cramer's Rule ✓and simplify to achieve the equation |adj(A)| = |A|^ - 1.
Transcribed Image Text:Let A be a nonsingular n x n matrix, with n ≥ 2. Prove the following formula. |adj(A)| = |A|-1 Since A is nonsingular, we know that ---Select--- A. adj(A) = |AT|A B. O adj(A) = |A|AT C. adj(A) = |A¹|A D.O adj(A) = 0 E. adj(A) = |A|A-1 = ---Select--- A is invertible A has an entire row consisting of zeros. A is equal to its transpose the determinant of A is zero Taking the determinant of both sides of this equality and applying the property of a scalar multiple of a matrix gives which of the following? A.O ladj(A)I = = |A||A¹| BO ladj(A)| = |A|-^|A| В C.O ladj(A)| = |A||A| DO ladj(A): |A|-¹|A| O E. ladj(A)| = |A|T|A| To conclude, we apply |---Select--- ---Select--- Thus, we can express the adjoint of A as which of the following? the determinant of an inverse matrix property the determinant of a transpose property. the determinant of a matrix product property Cramer's Rule ✓and simplify to achieve the equation |adj(A)| = |A|^ - 1.
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