1. Compute the following and sketch the corresponding vectors.
a. u+v
b. v−w
c. −2u
d. u+2w
2. Find two different linear combinations of:
u=1−26,v=04−1
3. Express the given vector equation as a linear system.
a. x1[3−4]+x2[−17]=[−30]
b. x120−3+x26−13+x3130=443
4. Express the given linear system as a vector equation.
a. x1+3x2=5
−2x1+3x2=−1
b. 5x1−x2+2x3=−4
2x1−x3=3
−x1+3x2+7x3=0
2x1+3x2−x3=−2
a. 4x1+5x2−3x3=−2
−x1+3x2+5x3=−8
x1+3x23x4−5x5x3−6x4+10x53x4−4x5=5=−7=6
b.
6. Express b as a linear combination of a1 and a2 if possible where:
a1=[−12],a2=[30],b=[21]
7. Express b as a linear combination of a1,a2 and a3 if possible where:
a1=101,a2=210,a3=1−31,b=971
8. Express b as a linear combination of a1,a2 and a3 if possible where:
a1=101,a2=210,a3=−11−3,b=613