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>If any two rows or columns of a determinant are equal, then its value is zero. If each element of a row or column of a determinant multiplied by k, then its value is multiplied by k. If two rows or columns of determinant are proportional, the value of the determinant is zero. A..
>If any two rows or columns of a determinant are equal, then its value is zero. If each element of a row or column of a determinant multiplied by k, then its value is multiplied by k. If two rows or columns of determinant are proportional, the value of the determinant is zero. A..Consistency of a system of linear equation
The above discussion leads to find the solution of a system of linear equations in two variables by using Cramer's rule. Cramer's rule suggests the use of determinants to solve a system of linear equations. Let us denote a 1 b 2 - a 2 b 1 (Denominators of ..
The above discussion leads to find the solution of a system of linear equations in two variables by using Cramer's rule. Cramer's rule suggests the use of determinants to solve a system of linear equations. Let us denote a 1 b 2 - a 2 b 1 (Denominators of ..Sequences and Series Examples
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, ..
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, ..Half of a herd of camels was seen in a forest. 2 times the square root..
Half of a herd of camels was seen in a forest. 2 times the square root of the herd had gone to the mountain slopes. 728 camels were on the bank of a river. What was the total number of camels in the herd? => 105 or 14 or 106 or 104..
Aid to memorise the table for standard angles:
(a) Write 0, 1, 2, 3, 4 over each column as shown above. (b) Divide each number by 4 and take the square root. The values obtained are sine ratios. (c) Write these ratios in reverse order and you obtain the cosine ratios (sin A = cos B if..
(a) Write 0, 1, 2, 3, 4 over each column as shown above. (b) Divide each number by 4 and take the square root. The values obtained are sine ratios. (c) Write these ratios in reverse order and you obtain the cosine ratios (sin A = cos B if..Linear Equations in One Variable
Linear Equations in One Variable - An equation of one variable and of first order (i.e., its highest power is one) is called a Linear equation. Such an equation has only one solution. A solution is also called the 'root' of the given equation.An equation of one variable and of first order..
Linear Equations in One Variable - An equation of one variable and of first order (i.e., its highest power is one) is called a Linear equation. Such an equation has only one solution. A solution is also called the 'root' of the given equation.An equation of one variable and of first order..Summary
>If any two rows or columns of a determinant are equal, then its value is zero. If each element of a row or column of a determinant multiplied by k, then its value is multiplied by k. If two rows or columns of determinant are proportional, the value of the determinant is zero. A..
>If any two rows or columns of a determinant are equal, then its value is zero. If each element of a row or column of a determinant multiplied by k, then its value is multiplied by k. If two rows or columns of determinant are proportional, the value of the determinant is zero. A..The time t to reach the ground for a freely falling body varies as the..
The time t to reach the ground for a freely falling body varies as the square root of the height h through which it is falling. Express t as a power function of h with a constant of proportion 2 g . => t = h or t = 2 h g or t = 2 g h or t ..
Find the value of k if f(x)= 12xsin 4x + kif x> 0,= 12if x≤..
Find the value of k if f ( x ) = 1 2 x sin 4 x + k if x > 0, = 12 if x ≤ 0 and lim x → 0 f ( x )..
Square ABCD is dilated by a scale factor of 2 with the center of dilat..
Square ABCD is dilated by a scale factor of 2 with the center of dilation at (0, 0). What will be the area of the new square? => It is 4 times the area of square ABCD. or It is 2 times the area of squareh..
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