(b) The rank of the matrix A is 2. 2 4 2 A =1 k 3 \1 2 2 Determine the value of the constant k. (i) (ii) For this value of k, is A invertible? Explain.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.8: Solving Systems With Cramer's Rule
Problem 1SE: Explain why we can always evaluate the determinant of a square matrix.
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(b) The rank of the matrix A is 2.
2 4 2
A = | 1
k 3
\1
2 2/
Determine the value of the constant k.
(i)
(ii)
For this value of k, is A invertible? Explain.
(c) Determine the definiteness of the quadratic form
q(x) = xỉ + 2v6x,x2 + 2x3
Transcribed Image Text:(b) The rank of the matrix A is 2. 2 4 2 A = | 1 k 3 \1 2 2/ Determine the value of the constant k. (i) (ii) For this value of k, is A invertible? Explain. (c) Determine the definiteness of the quadratic form q(x) = xỉ + 2v6x,x2 + 2x3
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