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 2020-10-27 Answered
If possible, find scalars c1,c2, and c3 so that
c1[123]+c2[111]+c3[141]=[223]
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Delorenzoz
Answered 2020-10-28 Author has 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.
Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2022-01-29 Author has 2047 answers
Jeffrey Jordon
Answered 2022-01-29 Author has 2047 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-02-08
Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.
asked 2021-01-31
Find a basis for the space of 2×2 diagonal matrices.
Basis ={[],[]}
asked 2021-01-13
write B as a linear combination of the other matrices, if possible.
B=[[2,2,3],[0,0,2],[0,0,2]]
A1=[[1,0,0],[0,1,0],[0,0,1]]
A2=[[0,1,1],[0,0,1],[0,0,0]]
A3=[[1,0,1],[0,1,0],[0,0,1]]
A4=[[1,1,1],[0,1,1],[0,0,1]]
asked 2021-06-27

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic. x12345678910f(x)2.42.883.4564.1474.9775.9727.1668.610.3212.383

asked 2021-01-04
If A is diagonalizable and for all eigenvalues , λ of A,|λ|=1 , then A is unitary. True or False?
asked 2020-11-11
Prove that if A and B are similar n x n matrices, then tr(A) = tr(B).
asked 2020-11-24
Use a software program or a graphing utility with matrix capabilities to find the transition matrix from B to B