# Topic: Chapter 7: Matrices and Determinants (Test 1)

Topic: Chapter 7: Matrices and Determinants
Q.1
If aij = 1/2 (3i − 2j ) and A = [a ij] 2×2 is
A. B. C. D. Explaination / Solution: Workspace
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Q.2
What must be the matrix X, if A. B. C. D. Explaination / Solution: Workspace
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Q.3
Which one of the following is not true about the matrix A. a scalar matrix
B. a diagonal matrix
C. an upper triangular matrix
D. a lower triangular matrix
Explaination / Solution:
No Explaination.

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Q.4
If A and B are two matrices such that A + B and AB are both defined, then

A. A and B are two matrices not necessarily of same order
B. A and B are square matrices of same order
C. Number of columns of A is equal to the number of rows of B
D. A = B.
Explaination / Solution: Workspace
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Q.5
If A = then for what value of λ, A2 = O ?
A. 0
B. ±1
C. - 1
D. 1
Explaination / Solution: Workspace
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Q.6
If and ( A + B )2 = A2 + B2 then the values of a and b are
A. a = 4, b = 1
B. a = 1, b = 4
C. a = 0, b = 4
D. a = 2, b = 4
Explaination / Solution: Workspace
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Q.7
If is a matrix satisfying the equation  AAT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to
A. (2, - 1)
B. (- 2, 1)
C. (2, 1)
D. (- 2, - 1)
Explaination / Solution: Workspace
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Q.8
If A is a square matrix, then which of the following is not symmetric?
A. A + AT
B. AAT
C.  AT
D. A − AT
Explaination / Solution: Workspace
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Q.9
If A and B are symmetric matrices of order n, where ( A ≠ B), then
A. A + B is skew-symmetric
B. A + B is symmetric
C. A + B is a diagonal matrix
D. A + B is a zero matrix
Explaination / Solution: Workspace
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Q.10
If A and if xy = 1, then det ( AAT ) is equal to
A. (a −1)2
B. (a2 +1)2
C.  a2 −1
D. (a2 −1)2 