Simplify the Matrix

Problem

3*[[0,0,2],[3,1,0],[0,−2,4]]−2*[[0,2,1],[3,0,5],[7,−6,0]]+8*[[1,−1,2],[3,4,5],[0,1,−1]]−4*[[0.25,1.25,0.5],[0.75,0.875,0.75],[−3.5,3.5,−1]]

Solution

1. Identify the dimensions of the matrices. The first three matrices are 3×3 The fourth matrix, as written in the prompt, contains inconsistent row lengths; interpreting the values as a 3×3 matrix based on standard notation for such problems (0.25, 1.25, 0.5e*t*c.),w*e*p*r*o*c*e*e*d(w)*i*t*h \times 3$ addition.

2. Distribute the scalar multipliers into each matrix.

3*[[0,0,2],[3,1,0],[0,−2,4]]=[[0,0,6],[9,3,0],[0,−6,12]]

−2*[[0,2,1],[3,0,5],[7,−6,0]]=[[0,−4,−2],[−6,0,−10],[−14,12,0]]

8*[[1,−1,2],[3,4,5],[0,1,−1]]=[[8,−8,16],[24,32,40],[0,8,−8]]

−4*[[0.25,1.25,0.5],[0.75,0.875,0.75],[−3.5,3.5,−1]]=[[−1,−5,−2],[−3,−3.5,−3],[14,−14,4]]

3. Sum the corresponding elements of the resulting matrices.

Row 1⇒[[0+0+8−1,0−4−8−5,6−2+16−2]]=[[7,−17,18]]

Row 2⇒[[9−6+24−3,3+0+32−3.5,0−10+40−3]]=[[24,31.5,27]]

Row 3⇒[[0−14+0+14,−6+12+8−14,12+0−8+4]]=[[0,0,8]]

Final Answer

3*[[0,0,2],[3,1,0],[0,−2,4]]−2*[[0,2,1],[3,0,5],[7,−6,0]]+8*[[1,−1,2],[3,4,5],[0,1,−1]]−4*[[0.25,1.25,0.5],[0.75,0.875,0.75],[−3.5,3.5,−1]]=[[7,−17,18],[24,31.5,27],[0,0,8]]

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