Solve the given system of equations, or else show that there is no solution. a) x1+2x2−x3=1 2x1+x2+x3=1 x1−x2+2x3=1 b) x1+2x2−x3=−2 −2x1−4x2+2x3=4 2x1+4x2−2x3=−4

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Solve the given system of equations, or else show that there is no solution.  a) x1+2x2−x3=1  2x1+x2+x3=1  x1−x2+2x3=1  b) x1+2x2−x3=−2  −2x1−4x2+2x3=4  2x1+4x2−2x3=−4

coolbananas03ok · Accepted Answer

Step 1 Consider the following system: x1+2x2−x3=1 2x1+x2+x3=1 x1−x2+2x3=1 Solve the system Write augmented matrix [12−1121111−121] R3−R1→R2−2R1 [12−110−33−10−330] R3−R2→ [12−110−33−10001] From the last row, we got 0=1 which is absqrt. Hence the system has no solution Step 2 Consider the following syste: x1+2x2−x3=−2 −2x1−4x2+2x3=4 2x1+4x2−2x3=−4 Solve the system Write the augmented matrix [12−1−2−2−42424−2−4] R2+2R1→R3−2R1 [12−1−200000000] From this, we get x1+2x2−x3=−2 Here, x2, x3 are free variables. So choose x2=s, x3=t, where s, t are any parameters. Then x1=−2−2s+t Hence the solution to the given system is (x1x2x3)=(−2−2s+tst), where s, t are any parameters

ocretz56 · Accepted Answer

Step 1  Part A  The coefficient matrix is :  A=[12−12111−12]  Now  det(A)=[12−12111−12]=1×(2+1)−2×(4−1)−1×(−2−1)  ⇒det(A)=3−6+3=0  Since det(A)=0, the matrix is not invertible and thus, has no solution.  Step 2  Part B:  The coefficient matrix is:  A=[12−1−2−4224−2]  Now  det(A)==[12−1−2−4224−2]=1×(8−8)−2×(4−4)−1×(−8+8)  ⇒det(A)=0+0+0=0  Since det(A)=0, the matrix is not invertible and thus, has no solution.

Solve the given system of equations, or else show that

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