If possible, find scalars c1,c2, and c3 so that c1[12−3]+c2[−111]+c3[−14−1]=[2−23]

Question

If possible, find scalars c1,c2, and c3 so that  c1[12−3]+c2[−111]+c3[−14−1]=[2−23]

Delorenzoz · Accepted Answer

Step 1  Consider the equation:  c1[12−3]+c2[−111]+c3[−14−1]=[2−23]…(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:  [c12c1−3c1]+[−c2c2c2]+[−c34c3−c3]=[2−23]…(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):  [c1−c2−c32c1+c2+4c3−3c1+c2−c3]=[2−23]  Step 4  Equating rows from both sides of matrices:  c1−c2−c3=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+c2−c3=3  −3(2+c2+c3)+c2−c3=3[∵From (3)]  −2c2−4c3=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 · Accepted Answer

Answer is given below (on video)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

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}

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