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Let A = be expressed as P + Q, where P is symmetric matrix and Q is Skew — symmetric matrix. Which one of the following is correct?
If the system of equations x — 2y — 3z = 1, ( P + 2 )z = 3, (2 P + l ) y + z = 2 inconsistent, then value of P is
The values of the minors of the elements of the first row of the determinant are respectively
The system of linear equation
x – y + 2z = b_{1}
x + 2y – z = b_{2}
2y – 2z = b_{3}_{ }
is inconsistent when (b_{1}, b_{2}, b_{3}) equals
The system of linear equation
x – y + 2z = b_{1}
x + 2y – z = b_{2}
2y – 2z = b_{2}
Apply
System is in consistent if
The system of equations
2x + 2y – 3z = 1,
4x + 4y + z = 2,
6x + 6y – z = 3 has
The matrix form of the system of equation is AX = b
The augmented matrix is
Applying R_{2 }→ R_{2}  2R1 , R_{3} → R_{3}  3R1, we have
Apply R_{3 }→ R_{3}  8R_{2}
Hence, the rank of the matrix is equal to 2 i.e. r ( A  b) = 2.
Here, rank(A) = 2 = rank[Ab] < no of unknowns = 3. So there are infinite many solution of the system of equations.
Square matrix A of order n over R has rank n. Which one of the following statement is not correct?
Since, if A is a square matrix of rank n, then it cannot be a singular
Which of the following statements is/are correct. The trace of a matrix A = is defined by Tr(A) = a_{11} + a_{22}
Correct Answer : a
Explanation : Properties of Transpose :
(A + B)^{T} = A^{T} + B^{T}
(kA)^{T} = kA^{T}
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