For which values of the constants c and d is begin{bmatrix}5 7c d end{bmatrix} a linear combination of begin{bmatrix}1 11 1 end{bmatrix} text{ and } begin{bmatrix}1 23 4 end{bmatrix}

snowlovelydayM 2021-02-12 Answered
For which values of the constants c and d is [57cd] a linear combination of [1111] and [1234]
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lobeflepnoumni
Answered 2021-02-13 Author has 99 answers
Step 1 Calculation: Write the vector [57cd] in linear combination of [1111] and [1234]
[57cd]=A[1111]+B[1234]
So we get four linear equations in A and B
{A+B=5A+2B=7A+3B=cA+4B=d
consider first two linear equations {A+B=5A+2B=7
By solving these equations we get A=3 , B=2
Now we have equations {A+3B=cA+4B=d
Substituting values A=3 , B=2 in above system we get {c=3+3(2)=9d=3+4(2)=11
c=9,d=11
Hence for c=9 , d=11 we can write the vector [57cd] in linear combination of [1111] and [1234] Step 2 Answer: Hence for c=9 , d=11 we can write the vector [57cd] in linear combination
of [1111] and [1234]
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Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

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