- COMMON ALGEBRA ERRORS–
995.The matrix equation has infinitely many solutions.
a.Since the determinant of the coefficient matrix is zero, the system has no solution.b.The system has a unique solution given by.
c.There is no error.a.The two matrices on the left side of the equality do not have the same dimension. As such, their sum is
undefined.
b.The matrices were added incorrectly. The right side should be.
c.There is no error.a.The product should be a real number, namely.
b.The inner dimension of the two matrices on the left side are not the same. As such, they cannot be
multiplied.
c.There is no error.- det = (2)(1) – (4)(–1) = 6
a.The wrong pairs of entries are being multiplied to form the determinant. The correct statementshould be det = (4)(2) – (1)(–1) = 9.b.The difference is computed in the wrong order. The correct statement should be det = (4)(–1)- (2)(1) = –6.
c.There is no error.
a.The constant multiple on the right side of the first equality should be 1, not –1. Therefore, the inverseshould be.
b.The inverse does not exist because several of the entries are the same real number.
c.There is no error.0
1
1
– 1
> – H
1
1
1
0
0
1
1
1
0
1
1
– – 1
–
–
- 1
HHH==
4
1
2
> – 1 H
4
1
2
> – 1 H
4
1
2
> – 1 H
99 ––––12 21CC. =+=( )( )^12 ( )( )2 1^4
99 ––12 2 1CC. =>– 42 –^12 H
0
1
0
0
1
> 0 H
0
1
0
0
1
0
0
1
1
0
>> >HHH+=
x
y2
4
1
2
2
–– 4
– (^1) –
HHH=
2
4
1
>–– 2 H
2
4
1
2
2
4
x
––y