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MTS 4B 04—LINEAR ALGEBRA
(Multiple Choice Questions for SDE Candidates)

If A and B are square matrices of the same order, then :

(AB)! =
(A) ATB?, ‏رص‎ Br AT
(೮) நந (D) (BA)?

A matrix that is both symmetric and upper triangular must be a:
(A) Diagonal matrix. (B) Non-diagonal but symmetric.
(C) Both (A) and (B). (D) None of the above.

If A and B are invertible matrices with the same size, then AB is invertible and (AB)~ =.

(A) ^ 181. (8) 2814 -1.
(ಲ) Both A and B. (D) None of the above.
A matrix E is called ———— if it can be obtained from an identity matrix by performing a single

elementary row operation.

(A) Equivalent matrix. (B) Echelon matrix.

(C) Elementary matrix. (D) Row reduced matrix.
A homogeneous linear system in unknowns whose corresponding augmented matrix has areduced
row echelon form with r leading 1’s has

(4) n-free variables (B) n-r free variables.

(0) r-free variables. (D) Cannot be determined.
A consistent linear system of two equations in two unknowns has :

(ಹಿ) Exactly one solution. (B) Infinitely many solutions.

(C) Exactly two solutions. (D) Hither (A) or (B).
If T, :R” > R” and Tp: R” >R” are matrix transformations, and if Ty («)=Tp (x) for every
vector x in R”, then :

(A) (A) and (B) are equivalent but not equal.

(B) (A) and (B) are equal.

(C) (A) and (B) cannot be equal.

(D) Cannot be determined.

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