Two matrices are equal when each element in the first matrix equals the corresponding element in the same position in the second matrix.
[x+y1+z4y]=[2546]
Comparing corresponding positions:
Top-left: x+y=2 ... (1)
Top-right: 4=4 ✓
Bottom-left: 1+z=5 ... (2)
Bottom-right: y=6 ... (3)
From equation (3):
y=6
From equation (2):
1+z=5
z=5−1
z=4
From equation (1), substituting y=6:
x+6=2
x=2−6
x=−4
Therefore: x=−4, y=6, z=4