CBSE Class 12 (Commerce) Determinants — practice questions
91 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 12 (Commerce) Determinants in the app →A determinant can be associated with which kind of matrix?Determinants here are studied up to which order?Expanding a determinant along different rows gives:For easier work, expand along the row or column with most:A determinant of zero means the matrix is:A matrix whose determinant is not zero is called:The area of a triangle with three collinear points is:The minor of an element is found by deleting its:The minor of an element in an order n determinant has order:The cofactor Aij equals the minor multiplied by:Before finding the inverse of a matrix, we first define its:A square matrix is invertible if and only if it is:If A and B are non-singular of the same order, then AB is:Since area is positive, we take which value of the determinant?If A = kB for square matrices of order n, then det A equals:For a 2 by 2 matrix with A = 2B, det A is det B times:Three points are collinear when the determinant of their coordinates is:When the area is given and you must find a coordinate, use:A determinant may be thought of as a function from matrices to:A determinant can be associated with a matrix that is:The determinant of a square matrix is a:The determinant may be viewed as a function whose output is:Vertical bars around A are read as the determinant of A, not the:The determinant of a matrix of order one is worked out from:A matrix of order two by two holds entries numbering:A matrix of order three by three holds entries numbering:A determinant of order three is worked out by expressing it in terms:Interchanging the rows and columns of a determinant leaves it:The area of a triangle whose three points are collinear is:Deleting a row and a column of a determinant gives an element's:A minor with a sign attached to it gives the element's:Determinants are used to find the area of a:Determinants are used to find the inverse of a square:Systems of linear equations can be solved using the inverse of a:Determinants can solve systems in two or three:A matrix that is not square has a determinant that is:The determinant of a matrix may be a number that is:The signed minor of an element is written using which letter:Which of these is worked out first, before the cofactor?The adjoint of a matrix is assembled out of its:Determinants take each square matrix to exactly how many values?Evaluate the second order determinant with rows (2, 4) and (-1, 2).What is the value of the determinant with rows (x, x+1) and (x-1, x)?A matrix of order one, [a], has a determinant equal to what?Which kind of matrix is the only kind that has a determinant?In the notation |A|, how is the symbol read for a matrix A?How many different row or column expansions give a 3 by 3 determinant?Expanding a 3 by 3 determinant along any row or column gives what?Which sign factor multiplies the element in row 2, column 3 when expanding?To reduce work, along which line should a determinant be expanded?If A = 2B for 3 by 3 matrices and |B| = 4, find |A|.A 3 by 3 matrix has determinant -2. What is the determinant of twice it?What is the determinant of the 3 by 3 identity matrix?Find the determinant of the upper triangular matrix with rows (2, 5, 1), (0, 3, 4) and (0, 0, -1).What is the determinant of the diagonal matrix with entries 2, -3 and 4?A determinant equals 7. What does it become if two rows are interchanged?A determinant with two identical rows has what value?If every entry in one column of a matrix is zero, its determinant is?How does the determinant of a matrix compare with that of its transpose?Multiplying one row of a determinant of value 4 by 3 gives what value?Adding a multiple of one row to another row changes the determinant how?If |A| = 3 and |B| = -4 for same-order matrices, find |AB|.A square matrix A is called singular when which condition holds?For what k is the matrix with rows (k, 2) and (3, 6) singular?The matrix with rows (3, k) and (6, 4) is singular. Find k.Minor of aij is defined as what?The cofactor Aij of an element is related to its minor Mij how?If the minor of a12 in a 3 by 3 determinant is 5, its cofactor is?For rows (1, 2, 3), (4, 5, 6), (7, 8, 9), find the minor of the entry 6.In rows (1, 2, 3), (4, 5, 6), (7, 8, 9), what is the cofactor of 6?The entries of one row times the cofactors of another row sum to what?Entries of a row times their own cofactors, summed, give what?Triangle area from its three vertices equals what multiple of a 3 by 3 determinant?Find the area of the triangle with vertices (0,0), (4,0) and (0,6).Vertices (1,1), (3,1) and (2,5) form a triangle of what area in square units?Three collinear points form a triangle of what area?For which k are (1,2), (3,4) and (k,8) collinear?If a triangle's area is given, which determinant values are used?Why is the absolute value taken for a triangle area from a determinant?Triangle (0,0), (6,0), (0,k) has area 9 square units. Find all k.How is adj A defined for a square matrix A?Find adj A for A with rows (2, 3) and (1, 4).A times adj A equals what for a square matrix A of order n?For a non-singular matrix A, the inverse equals what?For A with rows (1, 2) and (3, 4), what is the top-left entry of A inverse?A system of equations is called consistent when what is true?For AX = B with |A| nonzero, how is X found by the matrix method?If |A| = 0 and (adj A)B is not the zero matrix, what follows?If |A| = 0 and (adj A)B = O, the system AX = B is what?Solve 2x + y = 7 and x + y = 4 by the matrix method. Find x.Two linear equations in x and y have a unique solution when which holds?