show your solution, answer 8, 9 and 10 [2 1a18. LetA= 0 -1 3andB= 1За 0Find the value ofa if1a-2det(A) + det (B) = 14.9. Determine whether or ot each of the following homogeneous systems has a nonzerosolution. If the system has nontrivial solution, provide it.x+ y- z=02x – 3y + z= 0x- 4y+2z = 0(a)x+ y- z=D02x + 4y - z= 03x + 2y+ 2z = 0(b)X1 + 2x2 - 3x3+4x 02x - 3x2 +5xz - 7x4 05x, + 6x2 - 9x3 +8x 0(c)10. Find a sequence of elementary matrices that can be used to write the matrix in row-echelon form17a)5 10 -51-2 -1b)4-4-6 121

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Answered: [2 1 a 8. Let A=|0 -1 3 and B= 1 За 0…

Math

Algebra

[2 1 a 8. Let A=|0 -1 3 and B= 1 За 0 Find the value of a if 1 a -2 a 2 det(A) + det (B) = 14.

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.5: Cramer's Rule

Problem 35PS

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Question

show your solution, answer 8, 9 and 10

[2 1
a
1
8. Let
A= 0 -1 3
and
B= 1
За 0
Find the value of
a if
1
a
-2
det(A) + det (B) = 14.
9. Determine whether or ot each of the following homogeneous systems has a nonzero
solution. If the system has nontrivial solution, provide it.
x+ y- z=0
2x – 3y + z= 0
x- 4y+2z = 0
(a)
x+ y- z=D0
2x + 4y - z= 0
3x + 2y+ 2z = 0
(b)
X1 + 2x2 - 3x3+4x 0
2x - 3x2 +5xz - 7x4 0
5x, + 6x2 - 9x3 +8x 0
(c)
10. Find a sequence of elementary matrices that can be used to write the matrix in row-
echelon form
1
7
a)
5 10 -5
1
-2 -1
b)
4
-4
-6 12
1

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