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Linear Algebra quiz #3, Quizzes of Linear Algebra

Linear algebra quiz #3 of the linear algebra class

Typology: Quizzes

2023/2024

Uploaded on 02/17/2025

hunter-bambule
hunter-bambule 🇺🇸

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MAT253 POW #3 30 points Name _________________________________
No Work = No Credit
1) Use Cramer’s Rule to solve the following system of linear equations
{14𝑥21𝑦+14𝑧=7
21𝑥+14𝑦+7𝑧=5
28𝑥+7𝑦21 𝑧=6
2) Describe the additive inverse of a vector in the vector space for M1, 4
The additive inverse of the vector V=(V1 V2 V3 V4) in the vector space M1,4 is -V=(-V1 -V2 -V3 -V4)
I know you may want me to show
how I solved the determinants.
Although I did on this screen, I
realized it could not fit. I am also at
my grandparents and forgot my
digital pen. If you want it I can
provide proof. I was going to ask
for an extension but I noticed that
you don't for this.
pf3

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MAT 253 POW # 3 3 0 points Name _________________________________ No Work = No Credit

  1. Use Cramer’s Rule to solve the following system of linear equations {
  1. Describe the additive inverse of a vector in the vector space for M1, 4
  1. Provided that u 1 =(2, 4, 3), u 2 = (2, 4, 3) and u 3 = (-6, 4, 2), write v =(54, 12, 9) as a linear combination of u1 , u 2 and u3 , if possible.
  2. Determine whether the set of all fifth-degree polynomials, together with the standard operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails.