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Using only this definition of rank and properties of the determinants to simplify the calculations, without scaling the matrix, determine all possible values of the parameter t, so that the matrix A then has rank 3. t/3 -3/2 0 A = (-3/3 -nt t/2 -2t 3 Present, in writing, a mathematical argument that justifies your answer, including the development of the calculations and the properties used.

Using only this definition of rank and properties of the determinants to simplify the calculations, without scaling the matrix, determine all possible values of the parameter t, so that the matrix A then has rank 3. t/3 -3/2 0 A = (-3/3 -nt t/2 -2t 3 Present, in writing, a mathematical argument that justifies your answer, including the development of the calculations and the properties used.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following definitions. I. A submatrix of a matrix A is any smaller matrix, obtained by removing one or more rows and / or columns from A. II . The rank of an Am x n matrix can be defined as the largest integer, p, for which any of the submatrices p x p, of A, has a non- zero determinant. If A is square, with det (A) + 0, the rank of A is its number of rows (or columns). Using only this definition of rank and properties of the determinants to simplify the calculations, without scaling the matrix, determine all possible values of the parameter t, so that the matrix A then has rank 3. t/3 -3/2 A : -2t -3/3 -nt t/2 Present, in writing, a mathematical argument that justifies your answer, including the development of the calculations and the properties used.
Transcribed Image Text:Consider the following definitions. I. A submatrix of a matrix A is any smaller matrix, obtained by removing one or more rows and / or columns from A. II . The rank of an Am x n matrix can be defined as the largest integer, p, for which any of the submatrices p x p, of A, has a non- zero determinant. If A is square, with det (A) + 0, the rank of A is its number of rows (or columns). Using only this definition of rank and properties of the determinants to simplify the calculations, without scaling the matrix, determine all possible values of the parameter t, so that the matrix A then has rank 3. t/3 -3/2 A : -2t -3/3 -nt t/2 Present, in writing, a mathematical argument that justifies your answer, including the development of the calculations and the properties used.
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