Which 2x2 among the matrices/matrix below satisfy(ies) X^2 -5X + 21 = 0 where I and O are the 2x2 identity and zero matrices respectively? We are given that X satisfy the polynomial x² -Tr(X)x + det(X) where Tr(X) is its trace and its determinant, det(X), is ad-bc when first row is [a b] and second row is [c d]. Consider only the matrices given below: A is the matrix with first and 2nd rows [1 -1] and [-2 4] and B is the matrix with first and 2nd rows [4-1] and [-2 1]. {SHOW SOLUTION} 1 4 A = [²4] B =[ 21 -2 -2 choices: a) X = A only b) X = B only c) X = A or X = B d) X = A or X = B or X = (1/2)(A+B) e) X = A or X = B or X = (1/2)(A+B) or X = 2(A-B)
Which 2x2 among the matrices/matrix below satisfy(ies) X^2 -5X + 21 = 0 where I and O are the 2x2 identity and zero matrices respectively? We are given that X satisfy the polynomial x² -Tr(X)x + det(X) where Tr(X) is its trace and its determinant, det(X), is ad-bc when first row is [a b] and second row is [c d]. Consider only the matrices given below: A is the matrix with first and 2nd rows [1 -1] and [-2 4] and B is the matrix with first and 2nd rows [4-1] and [-2 1]. {SHOW SOLUTION} 1 4 A = [²4] B =[ 21 -2 -2 choices: a) X = A only b) X = B only c) X = A or X = B d) X = A or X = B or X = (1/2)(A+B) e) X = A or X = B or X = (1/2)(A+B) or X = 2(A-B)
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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![Which 2x2 among the matrices/matrix below satisfy(ies) X^2 -5X + 21 = 0
where I and O are the 2x2 identity and zero matrices respectively? We are
given that X satisfy the polynomial x² -Tr(X)x + det(X) where Tr(X) is its trace
and its determinant, det(X), is ad-bc when first row is [a b] and second row is
[c d]. Consider only the matrices given below:
A is the matrix with first and 2nd rows [1 -1] and [-2 4] and B is the matrix with
first and 2nd rows [4 -1] and [-2 1]. {SHOW SOLUTION}
A = [ ² ] B =[ 1
4
L-2
-2
choices:
a) X = A only
b) X = B only
c) X = A or X = B
d) X = A or X = B or X = (1/2)(A+B)
e) X = A or X = B or X = (1/2)(A+B) or X = 2(A-B)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6904e19-4c4f-4f9f-93e8-535fc97b98e7%2F502c0100-4739-4e6f-915a-ddb9189698c9%2F8npxep_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Which 2x2 among the matrices/matrix below satisfy(ies) X^2 -5X + 21 = 0
where I and O are the 2x2 identity and zero matrices respectively? We are
given that X satisfy the polynomial x² -Tr(X)x + det(X) where Tr(X) is its trace
and its determinant, det(X), is ad-bc when first row is [a b] and second row is
[c d]. Consider only the matrices given below:
A is the matrix with first and 2nd rows [1 -1] and [-2 4] and B is the matrix with
first and 2nd rows [4 -1] and [-2 1]. {SHOW SOLUTION}
A = [ ² ] B =[ 1
4
L-2
-2
choices:
a) X = A only
b) X = B only
c) X = A or X = B
d) X = A or X = B or X = (1/2)(A+B)
e) X = A or X = B or X = (1/2)(A+B) or X = 2(A-B)
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