a) Find the value(s) of k for the following matrix if the matrix is singular. -1 2 1 5 1 -4 -3 0 k b) Given A and B are 3x3 matrices, where |2A| = 16 and |B| = 9. Find |3(ATB)-¹|.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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QUESTION 3
a) Find the value(s) of k for the following matrix if the matrix is singular.
-1 5 1
(49)
2 -4 -3
1 0 k
b) Given A and B are 3x3 matrices, where |2A|
c) Consider the following system of linear equations where A is the coefficient matrix.
=
16 and |B| = 9. Find |3(A¹B)-¹|.
X1
2x1
5x₁ + 3x₂
X2 + 2x3
X2 + 3x3
+
4x3
-1
i) Find A-¹ by using the adjoint method.
ii) Solve for x3 by using Cramer's Rule.
=
=
122
14
= 32
Transcribed Image Text:QUESTION 3 a) Find the value(s) of k for the following matrix if the matrix is singular. -1 5 1 (49) 2 -4 -3 1 0 k b) Given A and B are 3x3 matrices, where |2A| c) Consider the following system of linear equations where A is the coefficient matrix. = 16 and |B| = 9. Find |3(A¹B)-¹|. X1 2x1 5x₁ + 3x₂ X2 + 2x3 X2 + 3x3 + 4x3 -1 i) Find A-¹ by using the adjoint method. ii) Solve for x3 by using Cramer's Rule. = = 122 14 = 32
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