If possible, find scalars c_1, c_2, text{ and } c_3 so that c_1begin{bmatrix}1 2-3 end{bmatrix}+c_2begin{bmatrix}-1 11 end{bmatrix}+c_3begin{bmatrix}-1 4-1 end{bmatrix}=begin{bmatrix}2 -23 end{bmatrix}

Wierzycaz

Wierzycaz

Answered question

2020-10-27

If possible, find scalars c1,c2, and c3 so that
c1[123]+c2[111]+c3[141]=[223]

Answer & Explanation

Delorenzoz

Delorenzoz

Skilled2020-10-28Added 91 answers

Step 1
Consider the equation:
c1[123]+c2[111]+c3[141]=[223](1)
Step 2
Now, when a matrix is multiplied by a scalar quantity, then all elements of matrix is multiplied by that scalar quantity.
Using this principle, rewrite equation (1) as:
[c12c13c1]+[c2c2c2]+[c34c3c3]=[223](2)
step 3
Now again,
Addition of matrices can be done by adding same position of elements together, thus creating a new single matrix.
From (2):
[c1c2c32c1+c2+4c33c1+c2c3]=[223]
Step 4
Equating rows from both sides of matrices:
c1c2c3=2
c1=2+c2+c3(3)
and
2c1+c2+4c3=2
2(2+c2+c3)+c2+4c3=2[From (3)]
3c2+6c3=6
c2+2c3=3(4)
Step 5
and
3c1+c2c3=3
3(2+c2+c3)+c2c3=3[From (3)]
2c24c3=9
c2+2c3=4.5(5)
From (4) and (5): Since L.H.S. of both equations are same but R.H.S. are not same, It is impossible to find the scalar quantity c1,c2 and c3.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-29Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-29Added 2605 answers

Answer is given below (on video)

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