Prove that the value of the determinant is real -7 5 + 3i 2/3 - 4i

5 - 3i 8 4 + 5i

2/3 + 4i 4 - 5i 9

Question

Prove that the value of the determinant is real -7 5 + 3i 2/3 -
4i
5 - 3i 8 4 + 5i
2/3 + 4i 4 - 5i 9

Anuradha Sharma · Accepted Answer

The given determinant is, =-75+3i23-4i5-3i84+5i23+4i4-5i9Now expanding the determinat along R1,=-772-4-5i4+5i-5+3i9×5-3i-4+5i23+4i+23-4i5-3i4-5i-823+4i=-772-16-25i2-5+3i45-27i-83-16i-10i3-20i2+23-4i20-25i-12i+15i2-163-32i=-731-5+3i1873-139i3+23-4i-69i-13  As we know that i2=-1=-217-9353+695i3-187i-139-46i-29-276+4i3=-217-9353-139-29-276-233i+233i=-217-9353-139-29-276That is a real term free from imaginary term i, you can further simplify for your own practice

Prove that the value of the determinant is real -7 5 + 3i 2/3 - 4i 5 - 3i 8 4 + 5i 2/3 + 4i 4 - 5i 9

Prove that the value of the determinant is real -7 5 + 3i 2/3 - 4i

5 - 3i 8 4 + 5i

2/3 + 4i 4 - 5i 9