MHT-CET Matrices — practice questions
83 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice MHT-CET Matrices in the app →A matrix is best described as which kind of arrangement of numbers?A matrix with 3 rows and 4 columns has which order?How many entries does a matrix of order 4 × 5 contain?In the notation aij, the subscript j tells the element's:A matrix of order 1 × n is known as a:An m × n matrix is a square matrix when:Another name for a matrix whose elements are all zero is:In a diagonal matrix, each element with i not equal to j is:Which square matrix has 1 on the main diagonal and 0 everywhere else?Two matrices of the same order are equal only if they also have:If [[x, 3], [2, y]] = [[5, 3], [2, 7]], then x + y equals:If [[2x + 1, 4], [0, 3]] = [[9, 4], [0, 3]], the value of x is:A 2 × 3 matrix and a 3 × 2 matrix share the same six entries. They are:The second row of [[1, 2], [3, 4]] + [[5, 6], [7, 8]] is:A zero matrix O of the same order satisfies A + O = A, so O is the additive:By the commutative law of addition, A + B always equals:If A = [[1, -2], [3, 0]], then 3A has first row:For A = [[2, 4], [6, 8]], the matrix (1/2)A is:For scalars k and l, the matrix (k + l)A equals:The rule k(A + B) = kA + kB holds when A and B have:The product AB exists only if the number of columns of A equals:If A is 2 × 3 and B is 3 × 4, the order of AB is:For A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], the product AB is:A row matrix [1 2 3] multiplied by the column with entries 4, 5, 6 gives:If the product AB is a zero matrix, then:The equation (AB)C = A(BC) states which law of multiplication?The identity A(B + C) = AB + AC is called the:For a square matrix A of order n, the product IA with identity I equals:If A = [[2, 0], [0, 3]], then A squared equals:The first row of [[2, 1], [1, 0]] times [[1, 2], [3, 4]] is:The transpose of a matrix is obtained by:If A has order 3 × 5, its transpose has order:Transposing a matrix twice, (A')', gives:For a constant k, the transpose (kA)' equals:Which of these matrices is symmetric?For A = [[1, 2], [4, 3]], the matrix (A + A')/2 has off-diagonal entry:For any square matrix A, the matrix A + A' is always:Any square matrix can be written as the sum of a symmetric matrix and a:A real matrix that is both symmetric and skew symmetric must be the:If B is the inverse of a square matrix A, then:A square matrix that possesses an inverse is called:For invertible matrices A and B of the same order, (AB) inverse equals:The inverse of the matrix [[2, 0], [0, 4]] is:If B is the inverse of A, then the inverse of B is:A matrix has 12 elements. Which order is impossible for it?How many different orders are possible for a matrix with 6 elements?In a 3 × 3 matrix with aij = i + j, the element a23 equals:A 2 × 2 matrix has aij = 2i - j. Its first row is:For the 2 × 2 matrix with aij = i × j, the sum of all elements is:A 3 × 3 diagonal matrix has all diagonal entries nonzero. How many zero entries does it have?A 4 × 4 scalar matrix has k = 5. The sum of all its elements is:If A is skew symmetric and a12 = 7, then a21 equals:For A = [[1, 2], [3, 4]], the diagonal entries of A - 2I add up to:For A = [[2, -1], [1, 0]], the expression A squared - 2A + I equals:For A of order m × n and B of order k × l, both AB and BA exist iff:In a product AB, the number of rows in the result equals the rows of:The difference A - B of two matrices is defined as:A square matrix A has an inverse exactly when which holds?How many distinct inverses can an invertible square matrix have?The adjoint of a square matrix A is obtained from the cofactor matrix by which operation?For a non-singular square matrix A, the product A(adj A) equals which matrix?Which formula gives the inverse of a non-singular matrix A by the adjoint method?What is the cofactor A12 of the entry 2 in the matrix with rows (1, 2) and (3, 4)?The adjoint of the matrix with rows (2, 5) and (1, 3) has which rows?The matrix with rows (2, 5) and (1, 3) has determinant 1. Its inverse has which rows?Which rows form the inverse of the matrix with rows (3, 1) and (5, 2)?In the inverse of the matrix with rows (3, 2) and (4, 3), what is the entry in row 1, column 2?For what value of k is the matrix with rows (k, 6) and (2, 4) singular?Can a matrix X exist with AX = I when A has rows (1, 2) and (2, 4)?In the uniqueness proof of the inverse, what do we assume at the start?Which transformation does the symbol Rj → Rj + kRi describe?After applying Rj → Rj + kRi to a matrix, which row stays exactly as it was?A matrix obtained from another by an elementary transformation is said to be what?Applying C1 → C1 + 2C3 to the matrix with rows (1, 0, 2) and (2, 3, 4) gives which first column?When a row operation is applied to a product AB, on which factor is it enough to apply it?To find A inverse by elementary steps, what is done to A?In the matrix equation AX = B for a system of equations, what does X hold?Which rows form the coefficient matrix for 2x + 3y = 5 and x - 4y = 9?Three linear equations in x, y and z are written as AX = B. What are the orders of A, X and B?By the method of inversion, the solution of AX = B is?For the method of inversion to solve three equations, what must be true of the coefficient matrix?Which pair names the two ways of solving AX = B using matrices?For the matrix with rows (1, 2) and (3, 4), A(adj A) equals which matrix?