Suppose
A =
4 3 5
1 3 −5
2 1 5
.
6.1 Evaluate det (A) by expanding along the 2nd row. NO marks will be awarded if you use any other
method.
(5)
6.2 Can Cramer’s rule be used to solve the system
A
x
y
z
=
0
0
a
where A is given and a 6= 0?
Give reasons for your answer. If the answer is Yes, use Cramer’s rule to solve the system. If not, use
any other method.
1
Expert's answer
2020-04-21T15:52:09-0400
We need to evaluate the determinant of matrix A using second row and also solve the system of equations by Cramer's rule .
The given matrix is
A=⎣⎡4123315−55⎦⎤
(6.1) Evaluation of the determinant of the given matrix A.
Determinant of A = det A = ∣∣4123315−55∣∣
=−1∣∣3155∣∣+3∣∣4255∣∣−(−5)∣∣4231∣∣
=−1(3×5−1×5)+3(4×5−2×5)+5(4×1−2×3)
=−1(15−5)+3(20−10)+5(4−6)
=−10+30−10=10
detA=10
(6.2). Solving of system of equation by using Cramer's rule
A⎣⎡xyz⎦⎤=⎣⎡00a⎦⎤anda=0
where, A=⎣⎡4123315−55⎦⎤
D=∣A∣=10=0
Yes, we can use the cramer's rule to solve the system of equations
Answer column is = ⎣⎡00a⎦⎤
Dx= coefficient determinant with answer-column values in x-column
=∣∣00a3315−55∣∣
=−0∣∣3155∣∣+3∣∣0a55∣∣−(−5)∣∣0a31∣∣
=0+3(0−5a)+5(0−3a)=−15a−15a=−30a
Dy= coefficient determinant with answer-column values in y-column
=∣∣41200a5−55∣∣
=−1∣∣0a55∣∣+0∣∣4255∣∣−(−5)∣∣420a∣∣
Dy=−1(0−5a)+0+5(4a−0)=5a+20a=25a
Dz= coefficient determinant with answer-column values in z-column
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