If [ array lll 1 & x & 1 array ] [ array ccc 1 & 3 & 2 2 & 5 & 1 15 & 3 & 2 array ] [ array l 1 2 x array ]=[0] then x is equal to

Step-by-step solution

Perform the matrix multiplication in two steps. First, multiply the row matrix by the 3 3 matrix: bmatrix 1 & x & 1 bmatrix bmatrix 1 & 3 & 2 2 & 5 & 1 15 & 3 & 2 bmatrix = bmatrix 1 + 2x + 15 & 3 + 5x + 3 & 2 + x + 2 bmatrix = bmatrix 16 + 2x & 6 + 5x & 4 + x bmatrix Now, multiply this result by the column matrix: bmatrix 16 + 2x & 6 + 5x & 4 + x bmatrix bmatrix 1 2 x bmatrix = [0] (16 + 2x)(1) + (6 + 5x)(2) + (4 + x)(x) = 0 16 + 2x + 12 + 10x + 4x + x^2 = 0 x^2 + 16x + 28 = 0 Factor the quadratic equation: (x + 1